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gateway/knowledge/trading/strategies/options/bear-call-ladder.md

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+---
+description: "A bullish-adjusted strategy selling a near-ATM call at K1 and buying two higher OTM calls at K2 and K3, arising when a bear call spread is adjusted for a stock that trades higher."
+tags: [options, hedging, bullish, ladder]
+---
+
+# Bear Call Ladder
+
+**Section**: 2.16 | **Asset Class**: Options | **Type**: Hedging
+
+## Overview
+The bear call ladder is a vertical spread consisting of a short call at K1 (near ATM), a long call at K2 (OTM), and a long call at K3 (further OTM, K3 > K2 > K1). A bear call ladder typically arises when a bear call spread goes wrong (the stock trades higher), so the trader buys another OTM call at K3 to adjust the position to bullish.
+
+## Construction
+- Sell 1 call option at strike K1 (near ATM)
+- Buy 1 call option at strike K2 (OTM, K2 > K1)
+- Buy 1 call option at strike K3 (further OTM, K3 > K2), same expiry
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = (S_T - K3)+ + (S_T - K2)+ - (S_T - K1)+ - H
+
+- Lower breakeven: S*_down = K1 - H  (if H < 0, net credit)
+- Upper breakeven: S*_up = K3 + K2 - K1 + H
+- Max profit: P_max = unlimited  (above S*_up)
+- Max loss: L_max = K2 - K1 + H  (in zone [K1, K2])
+
+## Key Conditions / Signals
+- Bullish adjustment to a bear call spread that has moved against the trader
+- Profits if the stock continues to rise significantly above K3
+- Low volatility near K1 environment after adjustment is undesirable
+
+## Notes
+The bear call ladder converts a bearish income strategy into a bullish capital gain strategy. The additional long call at K3 limits the maximum loss zone and creates profit on a sharp rally.

gateway/knowledge/trading/strategies/options/bear-call-spread.md

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+---
+description: "A bearish vertical spread selling a lower-strike OTM call at K2 and buying a higher-strike OTM call at K1 for a net credit, profiting if the stock stays below K2."
+tags: [options, income, bearish, vertical-spread]
+---
+
+# Bear Call Spread
+
+**Section**: 2.8 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The bear call spread is a vertical spread consisting of a long position in an OTM call option with strike K1, and a short position in another OTM call option with a lower strike K2 (K2 < K1). This is a net credit trade. The trader's outlook is bearish. This is an income strategy.
+
+## Construction
+- Buy 1 call option at strike K1 (higher OTM), same expiry
+- Sell 1 call option at strike K2 (lower OTM, K2 < K1)
+
+Net credit: C = premium received for K2 call - premium paid for K1 call
+
+## Payoff Profile
+f_T = (S_T - K1)+ - (S_T - K2)+ + C
+
+- Breakeven: S* = K2 + C
+- Max profit: P_max = C  (if S_T <= K2 at expiry; both calls expire worthless)
+- Max loss: L_max = K1 - K2 - C  (if S_T >= K1 at expiry)
+
+## Key Conditions / Signals
+- Bearish to neutral outlook; expects stock to remain below K2 by expiry
+- Prefer when implied volatility is elevated (larger credit received)
+- Income generation with defined upside risk
+
+## Notes
+The bear call spread is a credit spread. Maximum profit is limited to the net credit received. Maximum loss is the spread width minus the credit. The long call at K1 caps the loss relative to a naked short call.

gateway/knowledge/trading/strategies/options/bear-put-ladder.md

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+---
+description: "A bear put spread extended by selling an additional lower OTM put at K3, financing the spread while capping downside profit and creating unlimited risk below K3."
+tags: [options, income, bearish, ladder]
+---
+
+# Bear Put Ladder
+
+**Section**: 2.17 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The bear put ladder is a vertical spread consisting of a long put at K1 (near ATM), a short put at K2 (OTM, K2 < K1), and a short put at K3 (further OTM, K3 < K2). It is a bear put spread financed by selling an additional OTM put at K3. This adjusts the outlook from bearish (bear put spread) to conservatively bearish or even non-directional with an expectation of low volatility.
+
+## Construction
+- Buy 1 put option at strike K1 (near ATM)
+- Sell 1 put option at strike K2 (OTM, K2 < K1)
+- Sell 1 put option at strike K3 (further OTM, K3 < K2), same expiry
+
+Net debit or credit H  (assuming K3 + K2 - K1 + H > max(H, 0))
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (K2 - S_T)+ - (K3 - S_T)+ - H
+
+- Upper breakeven: S*_up = K1 - H  (if H > 0)
+- Lower breakeven: S*_down = K3 + K2 - K1 + H
+- Max profit: P_max = K1 - K2 - H  (achieved in zone [K3, K2])
+- Max loss: L_max = K3 + K2 - K1 + H  (unlimited as S_T -> 0)
+
+## Key Conditions / Signals
+- Conservatively bearish; expects stock to fall toward K2 but not collapse through K3
+- Low implied volatility environment expected after entry
+- The additional short put at K3 reduces cost but creates unlimited downside risk
+
+## Notes
+This is an income strategy in the sense that selling the K3 put finances the spread. However, unlimited loss exposure arises if the stock collapses well below K3. Risk management requires a stop-loss below K3.

gateway/knowledge/trading/strategies/options/bear-put-spread.md

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+---
+description: "A bearish vertical spread buying a near-ATM put at K1 and selling a lower-strike OTM put at K2 < K1 for a net debit, profiting if the stock falls toward K2."
+tags: [options, speculation, bearish, vertical-spread]
+---
+
+# Bear Put Spread
+
+**Section**: 2.9 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The bear put spread is a vertical spread consisting of a long position in a close to ATM put option with strike K1, and a short position in an OTM put option with a lower strike K2 (K2 < K1). This is a net debit trade. The trader's outlook is bearish: the strategy profits if the stock price falls. This is a capital gain strategy.
+
+## Construction
+- Buy 1 put option at strike K1 (near ATM), paying debit D
+- Sell 1 put option at strike K2 (OTM lower, K2 < K1), same expiry
+
+Net debit: D = premium paid for K1 put - premium received for K2 put
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (K2 - S_T)+ - D
+
+- Breakeven: S* = K1 - D
+- Max profit: P_max = K1 - K2 - D  (achieved when S_T <= K2)
+- Max loss: L_max = D  (if S_T >= K1 at expiry)
+
+## Key Conditions / Signals
+- Moderately bearish outlook; expects stock to fall toward or below K2 by expiry
+- Prefer when implied volatility is low (cheaper debit to enter)
+- Lower cost and lower risk than buying a naked put; downside profit is capped at K2
+
+## Notes
+Both profit and loss are limited. The maximum gain equals the spread width minus the net debit. Appropriate when the trader has a bearish view but wants to reduce the premium outlay compared to a simple long put.

gateway/knowledge/trading/strategies/options/bearish-long-seagull-spread.md

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+---
+description: "A bearish capital-gain strategy (short combo hedged by a long OTM call) buying an OTM put at K1, selling an ATM call at K2, and buying an OTM call at K3, ideally structured at zero cost."
+tags: [options, speculation, bearish, seagull]
+---
+
+# Bearish Long Seagull Spread
+
+**Section**: 2.55 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The bearish long seagull spread is a short combo (short risk reversal) hedged against the stock price rising by buying an OTM call option. It amounts to a long position in an OTM put at K1, a short position in an ATM call at K2, and a long position in an OTM call at K3 (K1 < K2 < K3). Ideally, the trade is structured to have zero cost. The trader's outlook is bearish. This is a capital gain strategy.
+
+## Construction
+- Buy 1 OTM put option at strike K1 (lowest)
+- Sell 1 ATM call option at strike K2 (middle)
+- Buy 1 OTM call option at strike K3 (highest, K3 > K2 > K1)
+- All same expiry; ideally zero net premium (H = 0)
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (S_T - K2)+ + (S_T - K3)+ - H
+
+Breakeven depends on sign of H:
+- S* = K1 - H  (if H > 0)
+- S* = K2 - H  (if H < 0)
+- K1 <= S* <= K2  (if H = 0)
+
+- Max profit: P_max = K1 - H  (if stock goes to zero; long put at full value)
+- Max loss: L_max = K3 - K2 + H  (if stock rises above K3; net short call capped at K3)
+
+## Key Conditions / Signals
+- Bearish outlook; expects stock to fall below K1
+- Ideally zero-cost (H = 0): the short call premium finances the long put
+- Long call at K3 caps the upside loss from the short call at K2
+
+## Notes
+The bearish long seagull is the mirror of the bullish short seagull spread. The long call at K3 hedges the unlimited upside risk of the short call at K2, capping maximum loss at K3 - K2 + H. The maximum profit is limited to K1 - H (stock to zero).

gateway/knowledge/trading/strategies/options/bearish-short-seagull-spread.md

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+---
+description: "A bearish capital-gain strategy (bear put spread financed by a short OTM call) selling an OTM call at K3, buying an ATM put at K2, and selling an OTM put at K1, ideally structured at zero cost."
+tags: [options, speculation, bearish, seagull]
+---
+
+# Bearish Short Seagull Spread
+
+**Section**: 2.56 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The bearish short seagull spread is a bear put spread financed with a sale of an OTM call option. It amounts to a short position in an OTM put at K1, a long position in an ATM put at K2, and a short position in an OTM call at K3 (K1 < K2 < K3). Ideally, the trade is structured to have zero cost. The trader's outlook is bearish. This is a capital gain strategy.
+
+## Construction
+- Sell 1 OTM put option at strike K1 (lowest)
+- Buy 1 ATM put option at strike K2 (middle)
+- Sell 1 OTM call option at strike K3 (highest, K3 > K2 > K1)
+- All same expiry; ideally zero net premium (H = 0)
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = -(K1 - S_T)+ + (K2 - S_T)+ - (S_T - K3)+ - H
+
+Breakeven depends on sign of H:
+- S* = K2 - H  (if H > 0)
+- S* = K3 - H  (if H < 0)
+- K2 <= S* <= K3  (if H = 0)
+
+- Max profit: P_max = K2 - K1 - H  (if S_T <= K1; bear put spread at max, put not needed)
+- Max loss: L_max = unlimited  (stock rises without bound above K3; short call exposed)
+
+## Key Conditions / Signals
+- Bearish outlook; expects stock to fall below K2 toward K1
+- Ideally zero-cost (H = 0): the short call premium finances the bear put spread
+- Short call at K3 creates unlimited upside risk above K3
+
+## Notes
+Unlike the bearish long seagull (which buys a call to cap upside), the bearish short seagull sells a call at K3 to finance the bear put spread, resulting in unlimited upside loss. The short put at K1 caps the downside profit. Requires careful stop-loss management above K3.

gateway/knowledge/trading/strategies/options/bull-call-ladder.md

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+---
+description: "A bullish vertical spread extended by selling a second OTM call at K3 > K2, financing a bull call spread while capping upside and creating unlimited risk above K3."
+tags: [options, income, bullish, ladder]
+---
+
+# Bull Call Ladder
+
+**Section**: 2.14 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The bull call ladder is a vertical spread consisting of a long call at K1 (near ATM), a short call at K2 (OTM), and a short call at K3 (further OTM, K3 > K2 > K1). It is a bull call spread financed by selling an additional OTM call at K3. This adjusts the outlook from bullish (bull call spread) to conservatively bullish or even non-directional with an expectation of low volatility.
+
+## Construction
+- Buy 1 call option at strike K1 (near ATM)
+- Sell 1 call option at strike K2 (OTM)
+- Sell 1 call option at strike K3 (further OTM, K3 > K2 > K1), same expiry
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = (S_T - K1)+ - (S_T - K2)+ - (S_T - K3)+ - H
+
+- Lower breakeven: S*_down = K1 + H  (if H > 0)
+- Upper breakeven: S*_up = K3 + K2 - K1 - H
+- Max profit: P_max = K2 - K1 - H  (achieved in zone [K2, K3])
+- Max loss: L_max = unlimited  (if S_T >> K3)
+
+## Key Conditions / Signals
+- Conservatively bullish; expects stock to rise to around K2 but not blow through K3
+- Low implied volatility environment expected after entry
+- The additional short call at K3 reduces cost but creates unlimited upside risk
+
+## Notes
+This is an income strategy in the sense that selling the K3 call finances the spread. However, unlimited loss exposure arises if the stock surges well above K3. Risk management requires a stop-loss above K3.

gateway/knowledge/trading/strategies/options/bull-call-spread.md

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+---
+description: "A bullish vertical spread buying a near-ATM call at K1 and selling an OTM call at K2 > K1 for a net debit, capping both profit and loss."
+tags: [options, speculation, bullish, vertical-spread]
+---
+
+# Bull Call Spread
+
+**Section**: 2.6 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The bull call spread is a vertical spread consisting of a long position in a close to ATM call option with strike K1, and a short position in an OTM call option with a higher strike K2. This is a net debit trade. The trader's outlook is bullish: the strategy profits if the stock price rises. This is a capital gain strategy.
+
+## Construction
+- Buy 1 call option at strike K1 (near ATM), paying debit D
+- Sell 1 call option at strike K2 (OTM, K2 > K1), same expiry
+
+Net debit: D = premium paid for K1 call - premium received for K2 call
+
+## Payoff Profile
+f_T = (S_T - K1)+ - (S_T - K2)+ - D
+
+- Breakeven: S* = K1 + D
+- Max profit: P_max = K2 - K1 - D  (achieved when S_T >= K2)
+- Max loss: L_max = D  (if S_T <= K1 at expiry)
+
+## Key Conditions / Signals
+- Moderately bullish outlook; expects stock to rise toward or above K2 by expiry
+- Prefer when implied volatility is low (cheaper debit to enter)
+- Lower cost and lower risk than buying a naked call; upside is capped at K2
+
+## Notes
+Both profit and loss are limited. The maximum gain equals the spread width minus the net debit. This strategy is appropriate when the trader has a directional view but wants to reduce the premium outlay compared to a simple long call.

gateway/knowledge/trading/strategies/options/bull-put-ladder.md

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+---
+description: "A bearish-adjusted strategy selling a near-ATM put at K1 and buying two lower OTM puts at K2 and K3, arising when a bull put spread is adjusted for a stock that trades lower."
+tags: [options, hedging, bearish, ladder]
+---
+
+# Bull Put Ladder
+
+**Section**: 2.15 | **Asset Class**: Options | **Type**: Hedging
+
+## Overview
+The bull put ladder is a vertical spread consisting of a short put at K1 (near ATM), a long put at K2 (OTM), and a long put at K3 (further OTM, K3 < K2 < K1). A bull put ladder typically arises when a bull put spread goes wrong (the stock trades lower), so the trader buys another OTM put at K3 to adjust the position to bearish.
+
+## Construction
+- Sell 1 put option at strike K1 (near ATM)
+- Buy 1 put option at strike K2 (OTM, K2 < K1)
+- Buy 1 put option at strike K3 (further OTM, K3 < K2), same expiry
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = (K3 - S_T)+ + (K2 - S_T)+ - (K1 - S_T)+ - H
+
+- Upper breakeven: S*_up = K1 + H  (if H < 0, net credit)
+- Lower breakeven: S*_down = K3 + K2 - K1 - H
+- Max profit: P_max = K3 + K2 - K1 - H  (if S_T -> 0)
+- Max loss: L_max = K1 - K2 + H  (in zone [K2, K1])
+
+## Key Conditions / Signals
+- Bearish adjustment to a bull put spread that has moved against the trader
+- Profits if the stock continues to fall significantly below K3
+- Low volatility near K1 environment after adjustment is undesirable
+
+## Notes
+The bull put ladder converts a bullish income strategy into a bearish capital gain strategy. The additional long put at K3 limits the maximum loss zone and creates profit on a sharp decline.

gateway/knowledge/trading/strategies/options/bull-put-spread.md

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+---
+description: "A bullish vertical spread selling a higher-strike OTM put at K2 and buying a lower-strike OTM put at K1 for a net credit, profiting if the stock stays above K2."
+tags: [options, income, bullish, vertical-spread]
+---
+
+# Bull Put Spread
+
+**Section**: 2.7 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The bull put spread is a vertical spread consisting of a long position in an OTM put option with strike K1, and a short position in another OTM put option with a higher strike K2 (K2 > K1). This is a net credit trade. The trader's outlook is bullish. This is an income strategy.
+
+## Construction
+- Buy 1 put option at strike K1 (lower OTM), same expiry
+- Sell 1 put option at strike K2 (higher OTM, K2 > K1)
+
+Net credit: C = premium received for K2 put - premium paid for K1 put
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (K2 - S_T)+ + C
+
+- Breakeven: S* = K2 - C
+- Max profit: P_max = C  (if S_T >= K2 at expiry; both puts expire worthless)
+- Max loss: L_max = K2 - K1 - C  (if S_T <= K1 at expiry)
+
+## Key Conditions / Signals
+- Bullish to neutral outlook; expects stock to remain above K2 by expiry
+- Prefer when implied volatility is elevated (larger credit received)
+- Income generation with defined downside risk
+
+## Notes
+The bull put spread is a credit spread. Maximum profit is limited to the net credit received. Maximum loss is the spread width minus the credit. The long put at K1 provides downside protection relative to a naked short put.

gateway/knowledge/trading/strategies/options/bullish-long-seagull-spread.md

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+---
+description: "A bullish capital-gain strategy (long combo hedged by a long OTM put) buying an OTM put at K1, selling an ATM put at K2, and buying an OTM call at K3, ideally structured at zero cost."
+tags: [options, speculation, bullish, seagull]
+---
+
+# Bullish Long Seagull Spread
+
+**Section**: 2.57 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The bullish long seagull spread is a long combo (long risk reversal) hedged against the stock price falling by buying an OTM put option. It amounts to a long position in an OTM put at K1, a short position in an ATM put at K2, and a long position in an OTM call at K3 (K1 < K2 < K3). Ideally, the trade is structured to have zero cost. The trader's outlook is bullish. This is a capital gain strategy.
+
+## Construction
+- Buy 1 OTM put option at strike K1 (lowest)
+- Sell 1 ATM put option at strike K2 (middle)
+- Buy 1 OTM call option at strike K3 (highest, K3 > K2 > K1)
+- All same expiry; ideally zero net premium (H = 0)
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (K2 - S_T)+ + (S_T - K3)+ - H
+
+Breakeven depends on sign of H:
+- S* = K3 + H  (if H > 0)
+- S* = K2 + H  (if H < 0)
+- K2 <= S* <= K3  (if H = 0)
+
+- Max profit: P_max = unlimited  (stock rises above K3; long call gains without bound)
+- Max loss: L_max = K2 - K1 + H  (if stock falls below K1; bear put spread at max loss)
+
+## Key Conditions / Signals
+- Bullish outlook; expects stock to rise above K3
+- Ideally zero-cost (H = 0): the short put premium finances the long call
+- Long put at K1 caps the downside loss from the short put at K2
+
+## Notes
+The bullish long seagull is the mirror of the bearish short seagull spread. The long put at K1 hedges the downside risk of the short put at K2, capping maximum loss at K2 - K1 + H. The maximum profit is unlimited on the upside via the long call at K3.

gateway/knowledge/trading/strategies/options/bullish-short-seagull-spread.md

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+---
+description: "A bullish capital-gain strategy (bull call spread financed by a short OTM put) selling an OTM put at K1, buying an ATM call at K2, and selling an OTM call at K3, ideally structured at zero cost."
+tags: [options, speculation, bullish, seagull]
+---
+
+# Bullish Short Seagull Spread
+
+**Section**: 2.54 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The bullish short seagull spread is a bull call spread financed with a sale of an OTM put option. It amounts to a short position in an OTM put at K1, a long position in an ATM call at K2, and a short position in an OTM call at K3 (K1 < K2 < K3). Ideally, the trade is structured to have zero cost. The trader's outlook is bullish. This is a capital gain strategy.
+
+## Construction
+- Sell 1 OTM put option at strike K1 (lowest)
+- Buy 1 ATM call option at strike K2 (middle)
+- Sell 1 OTM call option at strike K3 (highest, K3 > K2 > K1)
+- All same expiry; ideally zero net premium (H = 0)
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = -(K1 - S_T)+ + (S_T - K2)+ - (S_T - K3)+ - H
+
+Breakeven depends on sign of H:
+- S* = K2 + H  (if H > 0)
+- S* = K1 + H  (if H < 0)
+- K1 <= S* <= K2  (if H = 0)
+
+- Max profit: P_max = K3 - K2 - H  (if S_T >= K3; bull call spread at max)
+- Max loss: L_max = K1 + H  (if stock goes to zero; full loss on short put)
+
+## Key Conditions / Signals
+- Bullish outlook; expects stock to rise above K2 toward K3
+- Ideally zero-cost (H = 0): the short put premium finances the bull call spread
+- Short put at K1 creates downside exposure below K1
+
+## Notes
+The seagull spread's name comes from its payoff diagram shape. The upside is capped at K3 - K2 - H. The short put at K1 adds risk if the stock falls sharply, but at zero cost it provides a funded bullish position. Unlike the long combo, there is a defined maximum profit.

gateway/knowledge/trading/strategies/options/calendar-call-spread.md

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+---
+description: "A horizontal spread buying a longer-dated ATM call at TTM T' and selling a shorter-dated ATM call at the same strike K with TTM T < T', profiting from time decay when stock stays near K."
+tags: [options, income, neutral, calendar-spread]
+---
+
+# Calendar Call Spread
+
+**Section**: 2.18 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The calendar call spread (horizontal spread) consists of a long position in a near-ATM call option with TTM T' and a short position in a call option with the same strike K but shorter TTM T < T'. This is a net debit trade. The trader's outlook is neutral to bullish. The best case at expiration of the short call (t = T) is if the stock price is right at the strike (S_T = K), maximizing the remaining value V of the long call.
+
+## Construction
+- Buy 1 call option at strike K, TTM T' (longer expiry)
+- Sell 1 call option at strike K, TTM T < T' (shorter expiry), same strike
+
+Net debit: D
+
+## Payoff Profile
+At t = T (expiry of short call), let V = value of the long call (expiring at T') assuming S_T = K:
+
+- P_max = V - D  (if S_T = K at short expiry)
+- L_max = D  (net debit paid)
+
+If S_stop-loss <= S_T <= K, the trader can roll by writing another call with strike K and TTM T1 < T'.
+
+## Key Conditions / Signals
+- Neutral to mildly bullish; expects stock to remain near K through T
+- Low volatility environment after entry is ideal (long vega on net position)
+- Best suited for income generation by repeatedly selling shorter-dated calls against the long call
+
+## Notes
+This strategy resembles the covered call strategy in structure. While maintaining the long call, the trader can generate income by periodically selling call options with shorter maturities. The stop-loss price S_stop-loss defines the level below which the entire position is unwound.

gateway/knowledge/trading/strategies/options/calendar-put-spread.md

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+---
+description: "A horizontal spread buying a longer-dated ATM put at TTM T' and selling a shorter-dated ATM put at the same strike K with TTM T < T', profiting from time decay when stock stays near K."
+tags: [options, income, neutral, calendar-spread]
+---
+
+# Calendar Put Spread
+
+**Section**: 2.19 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The calendar put spread (horizontal spread) consists of a long position in a near-ATM put option with TTM T' and a short position in a put option with the same strike K but shorter TTM T < T'. This is a net debit trade. The trader's outlook is neutral to bearish. The best case at expiration of the short put (t = T) is if the stock price is right at the strike (S_T = K), maximizing the remaining value V of the long put.
+
+## Construction
+- Buy 1 put option at strike K, TTM T' (longer expiry)
+- Sell 1 put option at strike K, TTM T < T' (shorter expiry), same strike
+
+Net debit: D
+
+## Payoff Profile
+At t = T (expiry of short put), let V = value of the long put (expiring at T') assuming S_T = K:
+
+- P_max = V - D  (if S_T = K at short expiry)
+- L_max = D  (net debit paid)
+
+If K <= S_T <= S_stop-loss, the trader can roll by writing another put with strike K and TTM T1 < T'.
+
+## Key Conditions / Signals
+- Neutral to mildly bearish; expects stock to remain near K through T
+- Low volatility environment after entry is ideal
+- Best suited for income generation by repeatedly selling shorter-dated puts against the long put
+
+## Notes
+This strategy resembles the covered put strategy in structure. While maintaining the long put, the trader can generate income by periodically selling put options with shorter maturities. The stop-loss price S_stop-loss defines the level above which the entire position is unwound.

gateway/knowledge/trading/strategies/options/call-ratio-backspread.md

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+---
+description: "A strongly bullish volatility strategy selling fewer near-ATM calls at K1 and buying more OTM calls at K2, with unlimited profit on a strong rally and limited loss in between."
+tags: [options, volatility, bullish, backspread]
+---
+
+# Call Ratio Backspread
+
+**Section**: 2.36 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The call ratio backspread consists of a short position in N_S close to ATM call options with strike K1, and a long position in N_L OTM call options with strike K2 (K2 > K1), where N_L > N_S. Typically N_L = 2, N_S = 1 or N_L = 3, N_S = 2. The trader's outlook is strongly bullish. This is a capital gain strategy.
+
+## Construction
+- Sell N_S call options at strike K1 (near ATM)
+- Buy N_L call options at strike K2 (OTM, K2 > K1, N_L > N_S), same expiry
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = N_L × (S_T - K2)+ - N_S × (S_T - K1)+ - H
+
+- Lower breakeven (if H < 0, net credit): S*_down = K1 - H/N_S
+- Upper breakeven: S*_up = (N_L × K2 - N_S × K1 + H) / (N_L - N_S)
+- Max profit: P_max = unlimited  (above the upper breakeven)
+- Max loss: L_max = N_S × (K2 - K1) + H  (in the zone near K2 where long calls are OTM but short calls are ITM)
+
+## Key Conditions / Signals
+- Strongly bullish; expects a significant rally above K2
+- Ideally entered as a credit (H < 0) so that profit is also made if stock stays below K1
+- Loss zone is bounded between the two breakevens
+
+## Notes
+The difference between call ratio backspread and ratio call spread: here N_L > N_S (more longs than shorts). The maximum loss occurs near K2 at expiry. If H < 0, the position profits if the stock stays well below K1 or surges well above the upper breakeven.

gateway/knowledge/trading/strategies/options/collar.md

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+---
+description: "A hedging strategy (fence) buying stock, buying an OTM put at K1, and selling an OTM call at K2 > K1, capping both upside and downside within a defined range."
+tags: [options, hedging, bullish, collar]
+---
+
+# Collar
+
+**Section**: 2.53 | **Asset Class**: Options | **Type**: Hedging
+
+## Overview
+The collar (a.k.a. "fence") is a covered call augmented by a long put option as insurance against the stock price falling. It amounts to buying stock, buying an OTM put at K1, and selling an OTM call at K2 (K2 > K1). The trader's outlook is moderately bullish. This is a capital gain strategy. Note: a short collar is a covered put augmented by a long call option.
+
+## Construction
+- Buy 1 share of stock at S0
+- Buy 1 OTM put option at strike K1 (K1 < S0), paying put premium
+- Sell 1 OTM call option at strike K2 (K2 > S0 > K1), receiving call premium
+
+Net debit or credit H (= D if net debit, = -C if net credit)
+
+## Payoff Profile
+f_T = S_T - S0 + (K1 - S_T)+ - (S_T - K2)+ - H
+
+- Breakeven: S* = S0 + H
+- Max profit: P_max = K2 - S0 - H  (if S_T >= K2; upside capped by short call)
+- Max loss: L_max = S0 - K1 + H  (if S_T <= K1; downside protected by long put)
+
+## Key Conditions / Signals
+- Moderately bullish; willing to cap upside in exchange for downside protection
+- Ideal when trader has existing long stock position and wants to protect gains
+- Often structured as zero-cost (H = 0) by choosing K1 and K2 such that premiums offset
+
+## Notes
+The collar sacrifices unlimited upside potential (capped at K2) in exchange for limiting downside loss (floored at K1). It is one of the most common hedging strategies for long equity holders. A zero-cost collar is popular for protecting unrealized gains.

gateway/knowledge/trading/strategies/options/covered-call.md

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+---
+description: "A buy-write strategy combining long stock with a short call at strike K, generating income by capping upside in exchange for premium collected."
+tags: [options, income, covered, bullish]
+---
+
+# Covered Call
+
+**Section**: 2.2 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The covered call (a.k.a. "buy-write") strategy amounts to buying stock and writing a call option with strike K against the long stock position. The trader's outlook is neutral to bullish. It has the same payoff as writing a naked put and allows the trader to generate income by periodically selling OTM call options while maintaining the long stock position.
+
+## Construction
+- Buy 1 share of stock at price S0
+- Sell 1 call option at strike K, receiving net credit C
+
+Net position: long stock + short call
+
+## Payoff Profile
+f_T = S_T - S_0 - (S_T - K)+ + C = K - S_0 - (K - S_T)+ + C
+
+- Breakeven: S* = S0 - C
+- Max profit: P_max = K - S0 + C  (achieved when S_T >= K)
+- Max loss: L_max = S0 - C  (if stock goes to zero)
+
+## Key Conditions / Signals
+- Neutral to mildly bullish outlook on the underlying
+- Elevated implied volatility makes collected premium more attractive
+- Suitable for income generation when the trader is comfortable capping upside at K
+
+## Notes
+The covered call strategy is equivalent to writing a put option (short/naked put) in terms of payoff. Upside is capped at K; downside risk is the full cost of the stock minus premium received.

gateway/knowledge/trading/strategies/options/covered-put.md

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+---
+description: "A sell-write strategy combining short stock with a short put at strike K, generating income while maintaining a neutral-to-bearish position."
+tags: [options, income, covered, bearish]
+---
+
+# Covered Put
+
+**Section**: 2.3 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The covered put (a.k.a. "sell-write") strategy amounts to shorting stock and writing a put option with strike K against the short stock position. The trader's outlook is neutral to bearish. It has the same payoff as writing a naked call and allows the trader to generate income by periodically selling OTM put options while maintaining the short stock position.
+
+## Construction
+- Short 1 share of stock at price S0
+- Sell 1 put option at strike K, receiving net credit C
+
+Net position: short stock + short put
+
+## Payoff Profile
+f_T = S0 - S_T - (K - S_T)+ + C = S0 - K - (S_T - K)+ + C
+
+- Breakeven: S* = S0 + C
+- Max profit: P_max = S0 - K + C  (achieved when S_T <= K)
+- Max loss: L_max = unlimited  (stock can rise without bound)
+
+## Key Conditions / Signals
+- Neutral to mildly bearish outlook on the underlying
+- Elevated implied volatility makes collected premium more attractive
+- Suitable for income generation when the trader is comfortable with unlimited upside risk
+
+## Notes
+The covered put strategy is symmetrical to the covered call strategy. The short stock position carries unlimited loss potential if the stock rises; the collected put premium provides only limited cushion.

gateway/knowledge/trading/strategies/options/covered-short-straddle.md

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+---
+description: "A bullish income strategy augmenting a covered call by also writing an ATM put at the same strike K, increasing income at the cost of additional downside exposure."
+tags: [options, income, bullish, covered, straddle]
+---
+
+# Covered Short Straddle
+
+**Section**: 2.32 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The covered short straddle amounts to augmenting a covered call by writing a put option with the same strike K and TTM as the sold call option, thereby increasing the income. The trader's outlook is bullish. This is a combination of: long stock + short call at K + short put at K.
+
+## Construction
+- Buy 1 share of stock at S0
+- Sell 1 call option at strike K, receiving credit
+- Sell 1 put option at strike K (same strike and expiry), receiving additional credit
+
+Net credit: C (total premium from both short options)
+
+## Payoff Profile
+f_T = S_T - S0 - (S_T - K)+ - (K - S_T)+ + C
+
+- Breakeven: S* = (1/2)(S0 + K - C)
+- Max profit: P_max = K - S0 + C  (if S_T = K at expiry)
+- Max loss: L_max = S0 + K - C  (if stock goes to zero; put assignment + stock loss)
+
+## Key Conditions / Signals
+- Bullish to neutral; expects stock to remain near or above K
+- High implied volatility; writing both options collects more premium
+- The additional short put increases income but also increases downside risk significantly
+
+## Notes
+The downside risk is substantially higher than a plain covered call because the short put adds to the loss if the stock falls below K. The maximum loss occurs if the stock goes to zero (stock loss + put assignment at K).

gateway/knowledge/trading/strategies/options/covered-short-strangle.md

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+---
+description: "A bullish income strategy augmenting a covered call (short call at K) by also writing an OTM put at strike K' < K, increasing income with a wider profit zone than a covered short straddle."
+tags: [options, income, bullish, covered, strangle]
+---
+
+# Covered Short Strangle
+
+**Section**: 2.33 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The covered short strangle amounts to augmenting a covered call by writing an OTM put option with strike K' (K' < K) and the same TTM as the sold call option (whose strike is K), thereby increasing the income. The trader's outlook is bullish.
+
+## Construction
+- Buy 1 share of stock at S0
+- Sell 1 call option at strike K
+- Sell 1 OTM put option at strike K' (K' < K, same expiry)
+
+Net credit: C (total premium from both short options)
+
+## Payoff Profile
+f_T = S_T - S0 - (S_T - K)+ - (K' - S_T)+ + C
+
+- Max profit: P_max = K - S0 + C  (if S_T >= K at expiry; call in money, put expires worthless)
+- Max loss: L_max = S0 + K' - C  (if stock goes to zero; put assigned at K', full stock loss)
+
+## Key Conditions / Signals
+- Bullish to neutral; expects stock to remain above K' and ideally above K
+- Lower downside risk than covered short straddle (OTM put vs. ATM put)
+- The OTM put provides a wider profit zone on the downside at the cost of lower premium collected
+
+## Notes
+The short OTM put at K' creates downside risk below K', but less immediate than in the covered short straddle (where the put is ATM). The maximum loss is reduced compared to the covered short straddle because K' < K.

gateway/knowledge/trading/strategies/options/diagonal-call-spread.md

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+---
+description: "A diagonal spread buying a deep ITM call at K1 with TTM T' and selling an OTM call at K2 with shorter TTM T < T', combining directional and time decay benefits."
+tags: [options, income, bullish, diagonal-spread]
+---
+
+# Diagonal Call Spread
+
+**Section**: 2.20 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The diagonal call spread consists of a long position in a deep ITM call option with strike K1 and TTM T', and a short position in an OTM call option with strike K2 and shorter TTM T < T' (K2 > K1). This is a net debit trade. The trader's outlook is bullish. At t = T let V be the value of the long call (expiring at T') assuming S_T = K2.
+
+## Construction
+- Buy 1 deep ITM call option at strike K1, TTM T' (longer expiry)
+- Sell 1 OTM call option at strike K2, TTM T < T' (shorter expiry, K2 > K1)
+
+Net debit: D
+
+## Payoff Profile
+At t = T (expiry of short call), let V = value of the long call (expiring at T') assuming S_T = K2:
+
+- P_max = V - D  (if S_T = K2 at short expiry)
+- L_max = D  (net debit paid)
+
+If S_stop-loss <= S_T <= K2, the trader can write another OTM call with TTM T1 < T'.
+
+## Key Conditions / Signals
+- Bullish outlook; expects stock to rise toward K2 by the short expiry
+- Low volatility environment after entry is ideal for maximizing time decay income
+- The deep ITM long call more closely mimics the underlying stock than an ATM call
+
+## Notes
+Similar to the calendar call spread but the deep ITM long call (unlike the close to ATM call in the calendar spread) more closely mimics the underlying stock, providing better protection against a sharp rise in the stock price. The trader can generate income by periodically selling OTM call options with shorter maturities.

gateway/knowledge/trading/strategies/options/diagonal-put-spread.md

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+---
+description: "A diagonal spread buying a deep ITM put at K1 with TTM T' and selling an OTM put at K2 with shorter TTM T < T', combining directional and time decay benefits."
+tags: [options, income, bearish, diagonal-spread]
+---
+
+# Diagonal Put Spread
+
+**Section**: 2.21 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The diagonal put spread consists of a long position in a deep ITM put option with strike K1 and TTM T', and a short position in an OTM put option with strike K2 and shorter TTM T < T' (K2 < K1). This is a net debit trade. The trader's outlook is bearish. At t = T let V be the value of the long put (expiring at T') assuming S_T = K2.
+
+## Construction
+- Buy 1 deep ITM put option at strike K1, TTM T' (longer expiry)
+- Sell 1 OTM put option at strike K2, TTM T < T' (shorter expiry, K2 < K1)
+
+Net debit: D
+
+## Payoff Profile
+At t = T (expiry of short put), let V = value of the long put (expiring at T') assuming S_T = K2:
+
+- P_max = V - D  (if S_T = K2 at short expiry)
+- L_max = D  (net debit paid)
+
+If K2 <= S_T <= S_stop-loss, the trader can write another OTM put with TTM T1 < T'.
+
+## Key Conditions / Signals
+- Bearish outlook; expects stock to fall toward K2 by the short expiry
+- Low volatility environment after entry is ideal for maximizing time decay income
+- The deep ITM long put more closely mimics the underlying short stock than an ATM put
+
+## Notes
+Similar to the calendar put spread but the deep ITM long put (unlike the close to ATM put in the calendar spread) more closely mimics the underlying stock, providing better protection against a sharp drop in the stock price. The trader can generate income by periodically selling OTM put options with shorter maturities.

gateway/knowledge/trading/strategies/options/long-box.md

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+---
+description: "An arbitrage/volatility strategy combining a long synthetic forward and a short synthetic forward (or bull call spread and bear put spread) at two strikes, locking in a fixed payoff of K1 - K2."
+tags: [options, arbitrage, neutral, box]
+---
+
+# Long Box
+
+**Section**: 2.52 | **Asset Class**: Options | **Type**: Arbitrage
+
+## Overview
+The long box strategy can be viewed as a combination of a long synthetic forward and a short synthetic forward, or as a combination of a bull call spread and a bear put spread. It consists of: a long ITM put at K1, a short OTM put at K2 (lower), a long ITM call at K2, and a short OTM call at K1. The trader's outlook is neutral. This is a capital gain strategy. We assume K1 >= K2 + D.
+
+## Construction
+- Buy 1 ITM put option at strike K1 (higher)
+- Sell 1 OTM put option at strike K2 (lower, K2 < K1)
+- Buy 1 ITM call option at strike K2 (same as short put strike)
+- Sell 1 OTM call option at strike K1 (same as long put strike)
+- All same expiry
+
+Net debit: D  (assumed K1 >= K2 + D)
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (K2 - S_T)+ + (S_T - K2)+ - (S_T - K1)+ - D
+    = K1 - K2 - D  (constant, regardless of S_T)
+
+- P_max = (K1 - K2) - D  (fixed payoff at all stock prices)
+
+## Key Conditions / Signals
+- Used primarily as an arbitrage strategy when the market price of the box (D) is less than the theoretical value (K1 - K2)
+- Also used as a tax strategy in some jurisdictions (see footnote 31 in the source)
+- No directional risk: the payoff is fixed regardless of stock price at expiry
+
+## Notes
+The long box has a deterministic payoff of K1 - K2 - D at expiry. If D < K1 - K2 (mispricing), this is a risk-free profit. In practice, transaction costs and bid-ask spreads must be considered. Can also be used as a synthetic loan.

gateway/knowledge/trading/strategies/options/long-call-butterfly.md

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+---
+description: "A neutral low-cost debit strategy buying an OTM call at K1, selling two ATM calls at K2, and buying an ITM call at K3 with equidistant strikes, profiting if stock stays near K2."
+tags: [options, income, neutral, butterfly]
+---
+
+# Long Call Butterfly
+
+**Section**: 2.40 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The long call butterfly is a sideways strategy consisting of a long OTM call at K1, a short position in two ATM calls at K2, and a long ITM call at K3. The strikes are equidistant: K2 - K3 = K1 - K2 = kappa. This is a relatively low cost net debit trade. The trader's outlook is neutral. This is a capital gain strategy.
+
+## Construction
+- Buy 1 call option at strike K1 (OTM, upper wing)
+- Sell 2 call options at strike K2 (ATM, body)
+- Buy 1 call option at strike K3 (ITM, lower wing, K3 < K2 < K1)
+- All same expiry; K2 - K3 = K1 - K2 = kappa (equidistant)
+
+Net debit: D
+
+## Payoff Profile
+f_T = (S_T - K1)+ + (S_T - K3)+ - 2 × (S_T - K2)+ - D
+
+- Lower breakeven: S*_down = K3 + D
+- Upper breakeven: S*_up = K1 - D
+- Max profit: P_max = kappa - D  (achieved at S_T = K2)
+- Max loss: L_max = D  (if S_T <= K3 or S_T >= K1)
+
+## Key Conditions / Signals
+- Neutral; expects stock to pin near K2 at expiry
+- Low implied volatility after entry reduces theta bleed on short options
+- Low cost structure makes it an efficient way to bet on stability
+
+## Variations
+
+### 2.40.1 Modified Call Butterfly
+A variation where the strikes are no longer equidistant; instead K1 - K2 < K2 - K3. This results in a sideways strategy with a bullish bias. We have:
+
+f_T = (S_T - K1)+ + (S_T - K3)+ - 2 × (S_T - K2)+ - D
+
+- Breakeven: S* = K3 + D  (single breakeven on the lower side)
+- Max profit: P_max = K2 - K3 - D  (at S_T = K2)
+- Max loss: L_max = D
+
+## Notes
+The equidistant butterfly has two breakevens symmetric around K2. The maximum profit is the wing width kappa minus the debit. Low-cost entry makes the risk/reward ratio attractive for neutral views.

gateway/knowledge/trading/strategies/options/long-call-condor.md

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+---
+description: "A neutral low-cost debit strategy using four calls with equidistant strikes K1 < K2 < K3 < K4, profiting if the stock stays between K2 and K3 at expiry."
+tags: [options, income, neutral, condor]
+---
+
+# Long Call Condor
+
+**Section**: 2.46 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The long call condor is a sideways strategy consisting of a long ITM call at K1, a short ITM call at K2 (higher), a short OTM call at K3, and a long OTM call at K4 (higher). All strikes are equidistant: K4 - K3 = K3 - K2 = K2 - K1 = kappa. This is a relatively low cost net debit trade. The trader's outlook is neutral. This is a capital gain strategy.
+
+## Construction
+- Buy 1 call option at strike K1 (ITM, lowest)
+- Sell 1 call option at strike K2 (ITM, K2 > K1)
+- Sell 1 call option at strike K3 (OTM, K3 > K2)
+- Buy 1 call option at strike K4 (OTM, highest, K4 > K3)
+- All same expiry; K2 - K1 = K3 - K2 = K4 - K3 = kappa (equidistant)
+
+Net debit: D
+
+## Payoff Profile
+f_T = (S_T - K1)+ - (S_T - K2)+ - (S_T - K3)+ + (S_T - K4)+ - D
+
+- Upper breakeven: S*_up = K4 - D
+- Lower breakeven: S*_down = K1 + D
+- Max profit: P_max = kappa - D  (if K2 <= S_T <= K3 at expiry)
+- Max loss: L_max = D  (if S_T <= K1 or S_T >= K4)
+
+## Key Conditions / Signals
+- Neutral; expects stock to remain in the middle zone [K2, K3] at expiry
+- Low implied volatility after entry; wider profit zone than a butterfly
+- Low cost entry makes it efficient for betting on a range-bound stock
+
+## Notes
+The condor is a wider version of the butterfly: it has a flat profit plateau between K2 and K3 instead of a single peak. The tradeoff is that the maximum profit (kappa - D) is the same as the butterfly but requires K2 != K3 (four distinct strikes).

gateway/knowledge/trading/strategies/options/long-call-synthetic-straddle.md

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+---
+description: "A volatility strategy shorting stock and buying two ATM calls at strike K, replicating a long straddle by replacing the long put with a synthetic put."
+tags: [options, volatility, neutral, synthetic, straddle]
+---
+
+# Long Call Synthetic Straddle
+
+**Section**: 2.28 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The long call synthetic straddle (the same as a long straddle with the put replaced by a synthetic put) amounts to shorting stock and buying two ATM (or nearest ITM) call options with strike K. The trader's outlook is neutral. This is a capital gain strategy. We assume S0 >= K and D > S0 - K.
+
+## Construction
+- Short 1 share of stock at S0
+- Buy 2 ATM call options at strike K, same expiry
+
+Net debit: D  (assumed D > S0 - K)
+
+## Payoff Profile
+f_T = S0 - S_T + 2 × (S_T - K)+ - D
+
+- Upper breakeven: S*_up = 2K - S0 + D
+- Lower breakeven: S*_down = S0 - D
+- Max profit: P_max = unlimited  (large move in either direction)
+- Max loss: L_max = D - (S0 - K)  (at S_T = K; intrinsic offset reduces loss)
+
+## Key Conditions / Signals
+- Neutral view; expects a large move in either direction
+- S0 >= K (stock at or above the call strike)
+- D > S0 - K prevents arbitrage
+- Useful when puts are expensive relative to calls (use calls to synthesize the straddle)
+
+## Notes
+The short stock position combined with two long calls replicates a straddle by put-call parity. The maximum loss is reduced by the amount S0 - K (intrinsic value of the synthetic put component).

gateway/knowledge/trading/strategies/options/long-combo.md

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+---
+description: "A bullish capital-gain strategy (long risk reversal) buying an OTM call at K1 and selling an OTM put at K2 < K1, profiting from a strong upward move."
+tags: [options, speculation, bullish, risk-reversal]
+---
+
+# Long Combo
+
+**Section**: 2.12 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The long combo (a.k.a. "long risk reversal") amounts to buying an OTM call option with strike K1 and selling an OTM put option with strike K2, where K1 > K2. The trader's outlook is bullish. This is a capital gain strategy.
+
+## Construction
+- Buy 1 OTM call option at strike K1
+- Sell 1 OTM put option at strike K2 (K2 < K1), same expiry
+
+Net debit or credit H (H = D if net debit, H = -C if net credit; K1 > K2)
+
+## Payoff Profile
+f_T = (S_T - K1)+ - (K2 - S_T)+ - H
+
+Breakeven depends on sign of H:
+- S* = K1 + H  (if H > 0, net debit)
+- S* = K2 + H  (if H < 0, net credit)
+- K2 <= S* <= K1  (if H = 0, zero-cost)
+
+- Max profit: P_max = unlimited
+- Max loss: L_max = K2 + H
+
+## Key Conditions / Signals
+- Strongly bullish outlook
+- Traders often structure as zero-cost (H = 0) by selecting K1 and K2 such that premiums offset
+- Profits from a large upward move; loses if stock falls below K2
+
+## Notes
+Unlike the long synthetic forward (where K1 = K2 = S0), the long combo uses out-of-the-money strikes on both legs, creating a gap zone [K2, K1] where the payoff is flat (equal to -H). Downside is limited to K2 + H if S_T goes to zero.

gateway/knowledge/trading/strategies/options/long-guts.md

@@ -0,0 +1,33 @@
+---
+description: "A volatility strategy buying an ITM call at K1 and an ITM put at K2 > K1, profiting from a large move in either direction at higher cost than a straddle."
+tags: [options, volatility, neutral, guts]
+---
+
+# Long Guts
+
+**Section**: 2.24 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The long guts is a volatility strategy consisting of a long position in an ITM call option with strike K1 and a long position in an ITM put option with strike K2 (K2 > K1). This is a net debit trade. Because both options are ITM, this strategy is more costly to establish than a long straddle position. The trader's outlook is neutral. This is a capital gain strategy. We assume D > K2 - K1.
+
+## Construction
+- Buy 1 ITM call option at strike K1
+- Buy 1 ITM put option at strike K2 (K2 > K1), same expiry
+
+Net debit: D  (assumed D > K2 - K1)
+
+## Payoff Profile
+f_T = (S_T - K1)+ + (K2 - S_T)+ - D
+
+- Upper breakeven: S*_up = K1 + D
+- Lower breakeven: S*_down = K2 - D
+- Max profit: P_max = unlimited  (stock can move far in either direction)
+- Max loss: L_max = D - (K2 - K1)  (if K1 <= S_T <= K2; intrinsic value offsets some debit)
+
+## Key Conditions / Signals
+- Neutral directional view; expects a very large move but uncertain of direction
+- More expensive than a straddle but the ITM options provide intrinsic value floor
+- Max loss is reduced by the intrinsic spread K2 - K1 relative to the full debit
+
+## Notes
+The assumption D > K2 - K1 prevents risk-free arbitrage. The intrinsic value of the ITM options (K2 - K1) offsets part of the debit, making the maximum loss smaller than for a straddle with the same debit D. Both options have positive delta at entry.

gateway/knowledge/trading/strategies/options/long-iron-butterfly.md

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+---
+description: "A neutral income strategy combining a bull put spread and a bear call spread around a central ATM strike K2, collecting net credit when stock stays near K2."
+tags: [options, income, neutral, butterfly, iron]
+---
+
+# Long Iron Butterfly
+
+**Section**: 2.44 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The "long" iron butterfly is a sideways strategy combining a bull put spread and a bear call spread. It consists of a long OTM put at K1, short ATM put and ATM call at K2, and long OTM call at K3. The strikes are equidistant: K2 - K1 = K3 - K2 = kappa. This is a net credit trade. The trader's outlook is neutral. This is an income strategy.
+
+## Construction
+- Buy 1 OTM put option at strike K1 (lower wing)
+- Sell 1 ATM put option at strike K2 (body)
+- Sell 1 ATM call option at strike K2 (body, same strike as put)
+- Buy 1 OTM call option at strike K3 (upper wing)
+- All same expiry; K2 - K1 = K3 - K2 = kappa (equidistant)
+
+Net credit: C
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (K2 - S_T)+ - (S_T - K2)+ + (S_T - K3)+ + C
+
+- Upper breakeven: S*_up = K2 + C
+- Lower breakeven: S*_down = K2 - C
+- Max profit: P_max = C  (if K1 <= S_T <= K3; both spreads expire worthless)
+- Max loss: L_max = kappa - C  (if S_T <= K1 or S_T >= K3)
+
+## Key Conditions / Signals
+- Neutral; expects stock to remain close to K2 through expiry
+- High implied volatility environment makes the collected credit larger
+- Defined risk on both sides unlike a short straddle
+
+## Notes
+The long iron butterfly achieves the same payoff as the short call butterfly or short put butterfly but is constructed using four legs across two spreads. The maximum loss is limited (kappa - C) unlike in a naked short straddle.

gateway/knowledge/trading/strategies/options/long-iron-condor.md

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+---
+description: "A neutral income strategy combining a bull put spread and a bear call spread with four equidistant OTM/ITM strikes, collecting net credit when stock stays between the inner strikes."
+tags: [options, income, neutral, condor, iron]
+---
+
+# Long Iron Condor
+
+**Section**: 2.50 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The long iron condor is a sideways strategy combining a bull put spread and a bear call spread. It consists of a long OTM put at K1, a short OTM put at K2, a short OTM call at K3, and a long OTM call at K4. All strikes are equidistant: K4 - K3 = K3 - K2 = K2 - K1 = kappa. This is a net credit trade. The trader's outlook is neutral. This is an income strategy.
+
+## Construction
+- Buy 1 OTM put option at strike K1 (lowest)
+- Sell 1 OTM put option at strike K2 (K2 > K1)
+- Sell 1 OTM call option at strike K3 (K3 > K2)
+- Buy 1 OTM call option at strike K4 (highest, K4 > K3)
+- All same expiry; K2 - K1 = K3 - K2 = K4 - K3 = kappa (equidistant)
+
+Net credit: C
+
+## Payoff Profile
+f_T = (K1 - S_T)+ + (S_T - K4)+ - (K2 - S_T)+ - (S_T - K3)+ + C
+
+- Upper breakeven: S*_up = K3 + C
+- Lower breakeven: S*_down = K2 - C
+- Max profit: P_max = C  (if K2 <= S_T <= K3 at expiry; all options expire worthless)
+- Max loss: L_max = kappa - C  (if S_T <= K1 or S_T >= K4)
+
+## Key Conditions / Signals
+- Neutral; expects stock to remain between K2 and K3 through expiry
+- High implied volatility makes the collected credit larger
+- Defined risk on both sides; popular for structured income trading
+
+## Notes
+The long iron condor is the most widely traded condor variant. It provides a wider profit zone than the iron butterfly (K2 to K3 instead of a single point) with the same defined-risk structure. Maximum loss is limited to kappa - C on either side.

gateway/knowledge/trading/strategies/options/long-put-butterfly.md

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+---
+description: "A neutral low-cost debit strategy buying an OTM put at K1, selling two ATM puts at K2, and buying an ITM put at K3 with equidistant strikes, profiting if stock stays near K2."
+tags: [options, income, neutral, butterfly]
+---
+
+# Long Put Butterfly
+
+**Section**: 2.41 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The long put butterfly is a sideways strategy consisting of a long OTM put at K1, a short position in two ATM puts at K2, and a long ITM put at K3. The strikes are equidistant: K3 - K2 = K2 - K1 = kappa. This is a relatively low cost net debit trade. The trader's outlook is neutral. This is a capital gain strategy.
+
+## Construction
+- Buy 1 put option at strike K1 (OTM, lower wing)
+- Sell 2 put options at strike K2 (ATM, body)
+- Buy 1 put option at strike K3 (ITM, upper wing, K3 > K2 > K1)
+- All same expiry; K3 - K2 = K2 - K1 = kappa (equidistant)
+
+Net debit: D
+
+## Payoff Profile
+f_T = (K1 - S_T)+ + (K3 - S_T)+ - 2 × (K2 - S_T)+ - D
+
+- Upper breakeven: S*_up = K3 - D
+- Lower breakeven: S*_down = K1 + D
+- Max profit: P_max = kappa - D  (achieved at S_T = K2)
+- Max loss: L_max = D  (if S_T >= K3 or S_T <= K1)
+
+## Key Conditions / Signals
+- Neutral; expects stock to pin near K2 at expiry
+- Low implied volatility after entry reduces theta bleed on short options
+- Low cost structure makes it an efficient way to bet on stability
+
+## Variations
+
+### 2.41.1 Modified Put Butterfly
+A variation where the strikes are no longer equidistant; instead K3 - K2 < K2 - K1. This results in a sideways strategy with a bullish bias. For H > 0 there is also S*_up = K3 - H. We have:
+
+f_T = (K1 - S_T)+ + (K3 - S_T)+ - 2 × (K2 - S_T)+ - H
+
+- Lower breakeven: S*_down = 2 × K2 - K3 + H
+- Max profit: P_max = K3 - K2 - H  (at S_T = K2)
+- Max loss: L_max = 2 × K2 - K1 - K3 + H
+
+## Notes
+The equidistant butterfly has two breakevens symmetric around K2. The maximum profit is the wing width kappa minus the debit. Low-cost entry makes the risk/reward ratio attractive for neutral views.

gateway/knowledge/trading/strategies/options/long-put-condor.md

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+---
+description: "A neutral low-cost debit strategy using four puts with equidistant strikes K1 < K2 < K3 < K4, profiting if the stock stays between K2 and K3 at expiry."
+tags: [options, income, neutral, condor]
+---
+
+# Long Put Condor
+
+**Section**: 2.47 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The long put condor is a sideways strategy consisting of a long OTM put at K1, a short OTM put at K2 (higher), a short ITM put at K3, and a long ITM put at K4 (highest). All strikes are equidistant: K4 - K3 = K3 - K2 = K2 - K1 = kappa. This is a relatively low cost net debit trade. The trader's outlook is neutral. This is a capital gain strategy.
+
+## Construction
+- Buy 1 put option at strike K1 (OTM, lowest)
+- Sell 1 put option at strike K2 (OTM, K2 > K1)
+- Sell 1 put option at strike K3 (ITM, K3 > K2)
+- Buy 1 put option at strike K4 (ITM, highest, K4 > K3)
+- All same expiry; K2 - K1 = K3 - K2 = K4 - K3 = kappa (equidistant)
+
+Net debit: D
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (K2 - S_T)+ - (K3 - S_T)+ + (K4 - S_T)+ - D
+
+- Upper breakeven: S*_up = K4 - D
+- Lower breakeven: S*_down = K1 + D
+- Max profit: P_max = kappa - D  (if K2 <= S_T <= K3 at expiry)
+- Max loss: L_max = D  (if S_T <= K1 or S_T >= K4)
+
+## Key Conditions / Signals
+- Neutral; expects stock to remain in the middle zone [K2, K3] at expiry
+- Low implied volatility after entry; wider profit zone than a butterfly
+- Low cost entry makes it efficient for betting on a range-bound stock
+
+## Notes
+The put condor has the same payoff structure as the call condor (by put-call parity). The flat profit plateau between K2 and K3 provides a wider target zone for pinning compared to a butterfly. Four distinct equidistant strikes are required.

gateway/knowledge/trading/strategies/options/long-put-synthetic-straddle.md

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+---
+description: "A volatility strategy buying stock and buying two ATM puts at strike K, replicating a long straddle by replacing the long call with a synthetic call."
+tags: [options, volatility, neutral, synthetic, straddle]
+---
+
+# Long Put Synthetic Straddle
+
+**Section**: 2.29 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The long put synthetic straddle (the same as a long straddle with the call replaced by a synthetic call) amounts to buying stock and buying two ATM (or nearest ITM) put options with strike K. The trader's outlook is neutral. This is a capital gain strategy. We assume S0 <= K and D > K - S0.
+
+## Construction
+- Buy 1 share of stock at S0
+- Buy 2 ATM put options at strike K, same expiry
+
+Net debit: D  (assumed D > K - S0)
+
+## Payoff Profile
+f_T = S_T - S0 + 2 × (K - S_T)+ - D
+
+- Upper breakeven: S*_up = S0 + D
+- Lower breakeven: S*_down = 2K - S0 - D
+- Max profit: P_max = unlimited  (large move in either direction)
+- Max loss: L_max = D - (K - S0)  (at S_T = K; intrinsic offset reduces loss)
+
+## Key Conditions / Signals
+- Neutral view; expects a large move in either direction
+- S0 <= K (stock at or below the put strike)
+- D > K - S0 prevents arbitrage
+- Useful when calls are expensive relative to puts (use puts to synthesize the straddle)
+
+## Notes
+The long stock combined with two long puts replicates a straddle by put-call parity. The maximum loss is reduced by the amount K - S0 (intrinsic value of the synthetic call component).

gateway/knowledge/trading/strategies/options/long-straddle.md

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+---
+description: "A volatility strategy buying an ATM call and an ATM put at the same strike K, profiting from a large move in either direction."
+tags: [options, volatility, neutral, straddle]
+---
+
+# Long Straddle
+
+**Section**: 2.22 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The long straddle is a volatility strategy consisting of a long position in an ATM call option and a long position in an ATM put option with the same strike K. This is a net debit trade. The trader's outlook is neutral (non-directional). This is a capital gain strategy that profits from a large move in either direction.
+
+## Construction
+- Buy 1 ATM call option at strike K
+- Buy 1 ATM put option at strike K, same expiry
+
+Net debit: D
+
+## Payoff Profile
+f_T = (S_T - K)+ + (K - S_T)+ - D
+
+- Upper breakeven: S*_up = K + D
+- Lower breakeven: S*_down = K - D
+- Max profit: P_max = unlimited  (stock can move far in either direction)
+- Max loss: L_max = D  (if S_T = K exactly at expiry; both options expire worthless)
+
+## Key Conditions / Signals
+- Neutral directional view; expects a large move but uncertain of direction
+- Low implied volatility environment makes the debit cheaper to enter
+- Ideal before high-impact events (earnings, central bank announcements)
+
+## Notes
+The maximum loss is limited to the net debit paid. The position benefits from a rise in implied volatility (long vega). Time decay (theta) works against the position; the stock must move enough to overcome the debit paid.

gateway/knowledge/trading/strategies/options/long-strangle.md

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+---
+description: "A volatility strategy buying an OTM call at K1 and an OTM put at K2 < K1, profiting from a large move in either direction at lower cost than a straddle."
+tags: [options, volatility, neutral, strangle]
+---
+
+# Long Strangle
+
+**Section**: 2.23 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The long strangle is a volatility strategy consisting of a long position in an OTM call option with strike K1 and a long position in an OTM put option with strike K2 (K2 < K1). This is a net debit trade. Because both options are OTM, this strategy is less costly to establish than a long straddle. The flipside is that the move required to reach a breakeven point is more significant. The trader's outlook is neutral. This is a capital gain strategy.
+
+## Construction
+- Buy 1 OTM call option at strike K1
+- Buy 1 OTM put option at strike K2 (K2 < K1), same expiry
+
+Net debit: D
+
+## Payoff Profile
+f_T = (S_T - K1)+ + (K2 - S_T)+ - D
+
+- Upper breakeven: S*_up = K1 + D
+- Lower breakeven: S*_down = K2 - D
+- Max profit: P_max = unlimited  (stock can move far in either direction)
+- Max loss: L_max = D  (if K2 <= S_T <= K1 at expiry; both options expire worthless)
+
+## Key Conditions / Signals
+- Neutral directional view; expects a very large move but uncertain of direction
+- Cheaper than a straddle but requires a larger price movement to profit
+- Ideal before high-impact events where an extreme move is anticipated
+
+## Notes
+The maximum loss zone is the range [K2, K1] where both options expire worthless. The position is long vega and short theta. Compared to a straddle, the strangle is cheaper to enter but needs a bigger move to profit.

gateway/knowledge/trading/strategies/options/long-synthetic-forward.md

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+---
+description: "A bullish capital-gain strategy buying an ATM call and selling an ATM put at the same strike K = S0, replicating a long forward contract on the underlying."
+tags: [options, speculation, bullish, synthetic]
+---
+
+# Long Synthetic Forward
+
+**Section**: 2.10 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The long synthetic forward amounts to buying an ATM call option and selling an ATM put option with the same strike K = S0. This can be a net debit or net credit trade; typically |H| << S0. The trader's outlook is bullish: this strategy mimics a long stock or futures position and replicates a long forward contract with delivery price K and the same maturity as the options. This is a capital gain strategy.
+
+## Construction
+- Buy 1 ATM call option at strike K = S0
+- Sell 1 ATM put option at strike K = S0, same expiry
+
+Net debit or credit H (H = D for net debit trade, H = -C for net credit trade)
+
+## Payoff Profile
+f_T = (S_T - K)+ - (K - S_T)+ - H = S_T - K - H
+
+- Breakeven: S* = K + H
+- Max profit: P_max = unlimited  (stock can rise without bound)
+- Max loss: L_max = K + H  (if stock goes to zero)
+
+## Key Conditions / Signals
+- Strongly bullish outlook seeking full participation in upside
+- Useful when the cost of direct stock purchase is prohibitive
+- Typically near-zero net premium (H is small relative to S0)
+
+## Notes
+The payoff is linear in S_T — identical to holding the stock (minus K + H). The downside is not limited; the position loses as the stock falls below K, just like a long stock position.

gateway/knowledge/trading/strategies/options/protective-call.md

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+---
+description: "A hedging strategy combining short stock with a long call at strike K >= S0, limiting upside loss on a short position while preserving downside profit."
+tags: [options, hedging, protective, bearish]
+---
+
+# Protective Call
+
+**Section**: 2.5 | **Asset Class**: Options | **Type**: Hedging
+
+## Overview
+The protective call (a.k.a. "married call" or "synthetic put") amounts to shorting stock and buying an ATM or OTM call option with strike K >= S0. The trader's outlook is bearish. The call option hedges the risk of the stock price rising, acting as insurance on the short stock position.
+
+## Construction
+- Short 1 share of stock at price S0
+- Buy 1 call option at strike K (K >= S0), paying net debit D
+
+Net position: short stock + long call
+
+## Payoff Profile
+f_T = S0 - S_T + (S_T - K)+ - D = S0 - K + (K - S_T)+ - D
+
+- Breakeven: S* = S0 - D
+- Max profit: P_max = S0 - D  (if stock goes to zero)
+- Max loss: L_max = K - S0 + D  (capped by the long call at strike K)
+
+## Key Conditions / Signals
+- Bearish on the underlying but seeking upside protection on the short
+- Elevated uncertainty or event risk where a sharp rise in the stock is possible
+- Useful when the trader wants to retain short stock exposure but limit loss from a rally
+
+## Notes
+The protective call is symmetrical to the protective put strategy. Academic literature on protective calls appears scarce. The debit paid for the call reduces the effective profit from stock depreciation.

gateway/knowledge/trading/strategies/options/protective-put.md

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+---
+description: "A hedging strategy combining long stock with a long put at strike K <= S0, limiting downside loss while preserving unlimited upside."
+tags: [options, hedging, protective, bullish]
+---
+
+# Protective Put
+
+**Section**: 2.4 | **Asset Class**: Options | **Type**: Hedging
+
+## Overview
+The protective put (a.k.a. "married put" or "synthetic call") amounts to buying stock and buying an ATM or OTM put option with strike K <= S0. The trader's outlook is bullish. The put option hedges the risk of the stock price falling, acting as insurance on the long stock position.
+
+## Construction
+- Buy 1 share of stock at price S0
+- Buy 1 put option at strike K (K <= S0), paying net debit D
+
+Net position: long stock + long put
+
+## Payoff Profile
+f_T = S_T - S0 + (K - S_T)+ - D = K - S0 + (S_T - K)+ - D
+
+- Breakeven: S* = S0 + D
+- Max profit: P_max = unlimited  (stock can rise without bound)
+- Max loss: L_max = S0 - K + D  (floor established at strike K)
+
+## Key Conditions / Signals
+- Bullish on the underlying but seeking downside protection
+- Elevated uncertainty or event risk (earnings, macro) where a sharp drop is possible
+- Useful when the trader wants to retain long stock exposure but limit catastrophic loss
+
+## Notes
+The protective put is the put-call parity complement to the covered call. The debit paid for the put reduces the effective profit from stock appreciation. The maximum loss is capped at S0 - K + D regardless of how far the stock falls.

gateway/knowledge/trading/strategies/options/put-ratio-backspread.md

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+---
+description: "A strongly bearish volatility strategy selling fewer near-ATM puts at K1 and buying more OTM puts at K2 < K1, with unlimited profit on a sharp decline and limited loss in between."
+tags: [options, volatility, bearish, backspread]
+---
+
+# Put Ratio Backspread
+
+**Section**: 2.37 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The put ratio backspread consists of a short position in N_S close to ATM put options with strike K1, and a long position in N_L OTM put options with strike K2 (K2 < K1), where N_L > N_S. Typically N_L = 2, N_S = 1 or N_L = 3, N_S = 2. The trader's outlook is strongly bearish. This is a capital gain strategy.
+
+## Construction
+- Sell N_S put options at strike K1 (near ATM)
+- Buy N_L put options at strike K2 (OTM lower, K2 < K1, N_L > N_S), same expiry
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = N_L × (K2 - S_T)+ - N_S × (K1 - S_T)+ - H
+
+- Upper breakeven (if H < 0): S*_up = K1 + H/N_S
+- Lower breakeven: S*_down = (N_L × K2 - N_S × K1 - H) / (N_L - N_S)
+- Max profit: P_max = N_L × K2 - N_S × K1 - H  (if stock goes to zero)
+- Max loss: L_max = N_S × (K1 - K2) + H  (in the zone near K2 where long puts are OTM but short puts are ITM)
+
+## Key Conditions / Signals
+- Strongly bearish; expects a significant decline below K2
+- Ideally entered as a credit (H < 0) so that profit is also made if stock stays above K1
+- Loss zone is bounded between the two breakevens
+
+## Notes
+The difference between put ratio backspread and ratio put spread: here N_L > N_S (more longs than shorts). The maximum loss occurs near K2 at expiry. If H < 0, the position profits if the stock stays well above K1 or collapses well below the lower breakeven.

gateway/knowledge/trading/strategies/options/ratio-call-spread.md

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+---
+description: "A neutral-to-bearish income strategy selling more near-ATM calls at K1 than ITM calls bought at K2 < K1, collecting premium with unlimited upside risk above the upper breakeven."
+tags: [options, income, neutral, ratio-spread]
+---
+
+# Ratio Call Spread
+
+**Section**: 2.38 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The ratio call spread consists of a short position in N_S close to ATM call options with strike K1, and a long position in N_L ITM call options with strike K2 (K2 < K1), where N_L < N_S. Typically N_L = 1, N_S = 2 or N_L = 2, N_S = 3. This is an income strategy if structured as a net credit trade. The trader's outlook is neutral to bearish.
+
+## Construction
+- Sell N_S call options at strike K1 (near ATM)
+- Buy N_L call options at strike K2 (ITM, K2 < K1, N_L < N_S), same expiry
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = N_L × (S_T - K2)+ - N_S × (S_T - K1)+ - H
+
+- Lower breakeven (if H > 0): S*_down = K2 + H/N_L
+- Upper breakeven: S*_up = (N_S × K1 - N_L × K2 - H) / (N_S - N_L)
+- Max profit: P_max = N_L × (K1 - K2) - H  (in zone [K2, K1] range)
+- Max loss: L_max = unlimited  (above the upper breakeven; net short calls)
+
+## Key Conditions / Signals
+- Neutral to mildly bearish; expects stock to remain below K1
+- Structured as a net credit when possible (income strategy)
+- High implied volatility makes the collected premium from extra short calls larger
+
+## Notes
+Unlike the call ratio backspread (where N_L > N_S), here N_L < N_S, so there is net short call exposure above K1 creating unlimited upside risk. The maximum profit is achieved if the stock stays in the [K2, K1] zone at expiry.

gateway/knowledge/trading/strategies/options/ratio-put-spread.md

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+---
+description: "A neutral-to-bullish income strategy selling more near-ATM puts at K1 than ITM puts bought at K2 > K1, collecting premium with unlimited downside risk below the lower breakeven."
+tags: [options, income, neutral, ratio-spread]
+---
+
+# Ratio Put Spread
+
+**Section**: 2.39 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The ratio put spread consists of a short position in N_S close to ATM put options with strike K1, and a long position in N_L ITM put options with strike K2 (K2 > K1), where N_L < N_S. Typically N_L = 1, N_S = 2 or N_L = 2, N_S = 3. This is an income strategy if structured as a net credit trade. The trader's outlook is neutral to bullish.
+
+## Construction
+- Sell N_S put options at strike K1 (near ATM)
+- Buy N_L put options at strike K2 (ITM, K2 > K1, N_L < N_S), same expiry
+
+Net debit or credit H
+
+## Payoff Profile
+f_T = N_L × (K2 - S_T)+ - N_S × (K1 - S_T)+ - H
+
+- Upper breakeven (if H > 0): S*_up = K2 - H/N_L
+- Lower breakeven: S*_down = (N_S × K1 - N_L × K2 + H) / (N_S - N_L)
+- Max profit: P_max = N_L × (K2 - K1) - H  (in zone [K1, K2])
+- Max loss: L_max = N_S × K1 - N_L × K2 + H  (if stock goes to zero; unlimited downside)
+
+## Key Conditions / Signals
+- Neutral to mildly bullish; expects stock to remain above K1
+- Structured as a net credit when possible (income strategy)
+- High implied volatility makes the collected premium from extra short puts larger
+
+## Notes
+Unlike the put ratio backspread (where N_L > N_S), here N_L < N_S, so there is net short put exposure below K1 creating unlimited downside risk. The maximum profit is achieved if the stock stays in the [K1, K2] zone at expiry.

gateway/knowledge/trading/strategies/options/short-call-butterfly.md

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+---
+description: "A neutral net credit strategy selling an ITM call at K1, buying two ATM calls at K2, and selling an OTM call at K3, profiting from a large move away from K2."
+tags: [options, volatility, neutral, butterfly]
+---
+
+# Short Call Butterfly
+
+**Section**: 2.42 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The short call butterfly is a volatility strategy consisting of a short ITM call at K1, a long position in two ATM calls at K2, and a short OTM call at K3. The strikes are equidistant: K3 - K2 = K2 - K1 = kappa. This is a net credit trade. In this sense it is an income strategy. However, the potential reward is sizably smaller than with a short straddle or short strangle (albeit with lower risk). The trader's outlook is neutral.
+
+## Construction
+- Sell 1 call option at strike K1 (ITM, lower wing)
+- Buy 2 call options at strike K2 (ATM, body)
+- Sell 1 call option at strike K3 (OTM, upper wing, K3 > K2 > K1)
+- All same expiry; K3 - K2 = K2 - K1 = kappa (equidistant)
+
+Net credit: C
+
+## Payoff Profile
+f_T = 2 × (S_T - K2)+ - (S_T - K1)+ - (S_T - K3)+ + C
+
+- Upper breakeven: S*_up = K3 - C
+- Lower breakeven: S*_down = K1 + C
+- Max profit: P_max = C  (if S_T <= K1 or S_T >= K3; all options at their extremes)
+- Max loss: L_max = kappa - C  (if S_T = K2 at expiry)
+
+## Key Conditions / Signals
+- Neutral; expects stock to move significantly away from K2 by expiry
+- High implied volatility environment; collect larger credit upfront
+- Lower risk than a short straddle or strangle but also lower reward
+
+## Notes
+The short call butterfly is the reverse of the long call butterfly. Credit is collected upfront and profit is achieved if the stock moves far enough from K2. The maximum loss is bounded by the wing width kappa minus the credit received.

gateway/knowledge/trading/strategies/options/short-call-condor.md

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+---
+description: "A neutral volatility strategy selling an ITM call at K1 and OTM call at K4 while buying calls at K2 and K3, collecting credit and profiting from a large move outside [K1, K4]."
+tags: [options, volatility, neutral, condor]
+---
+
+# Short Call Condor
+
+**Section**: 2.48 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The short call condor is a volatility strategy consisting of a short ITM call at K1, a long ITM call at K2, a long OTM call at K3, and a short OTM call at K4. All strikes are equidistant: K4 - K3 = K3 - K2 = K2 - K1 = kappa. This is a relatively low net credit trade. As with a short call butterfly, the potential reward is sizably smaller than with a short straddle or short strangle (albeit with lower risk). So this is a capital gain (rather than income) strategy. The trader's outlook is neutral.
+
+## Construction
+- Sell 1 call option at strike K1 (ITM, lowest)
+- Buy 1 call option at strike K2 (ITM, K2 > K1)
+- Buy 1 call option at strike K3 (OTM, K3 > K2)
+- Sell 1 call option at strike K4 (OTM, highest, K4 > K3)
+- All same expiry; K2 - K1 = K3 - K2 = K4 - K3 = kappa (equidistant)
+
+Net credit: C
+
+## Payoff Profile
+f_T = (S_T - K2)+ + (S_T - K3)+ - (S_T - K1)+ - (S_T - K4)+ + C
+
+- Upper breakeven: S*_up = K4 - C
+- Lower breakeven: S*_down = K1 + C
+- Max profit: P_max = C  (if S_T <= K1 or S_T >= K4)
+- Max loss: L_max = kappa - C  (if K2 <= S_T <= K3 at expiry)
+
+## Key Conditions / Signals
+- Neutral; expects stock to move significantly outside the [K1, K4] range
+- High implied volatility environment; collect larger credit upfront
+- Defined risk on both sides, making it safer than a short straddle
+
+## Notes
+The short call condor is the reverse of the long call condor. Net credit is collected and the strategy profits from large moves in either direction. Maximum loss is kappa - C, occurring if the stock stays in the middle zone [K2, K3].

gateway/knowledge/trading/strategies/options/short-call-synthetic-straddle.md

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+---
+description: "A sideways strategy buying stock and selling two ATM calls at strike K, replicating a short straddle by replacing the short put with a synthetic short put."
+tags: [options, income, neutral, synthetic, straddle]
+---
+
+# Short Call Synthetic Straddle
+
+**Section**: 2.30 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The short call synthetic straddle (the same as a short straddle with the put replaced by a synthetic put) amounts to buying stock and selling two ATM (or nearest OTM) call options with strike K. The trader's outlook is neutral. This is a capital gain strategy. We assume S0 <= K.
+
+## Construction
+- Buy 1 share of stock at S0
+- Sell 2 ATM call options at strike K, same expiry
+
+Net credit: C
+
+## Payoff Profile
+f_T = S_T - S0 - 2 × (S_T - K)+ + C
+
+- Upper breakeven: S*_up = 2K - S0 + C
+- Lower breakeven: S*_down = S0 - C
+- Max profit: P_max = K - S0 + C  (at S_T = K)
+- Max loss: L_max = unlimited  (stock can rise without bound; short 2 calls)
+
+## Key Conditions / Signals
+- Neutral view; expects stock to stay near K through expiry
+- S0 <= K (stock at or below the call strike)
+- High implied volatility makes the collected credit from the two short calls larger
+
+## Notes
+Unlimited loss on the upside due to the two short calls. The long stock provides partial offset against rising prices but is insufficient beyond the breakeven. Active management or stop-losses are essential.

gateway/knowledge/trading/strategies/options/short-combo.md

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+---
+description: "A bearish capital-gain strategy (short risk reversal) buying an OTM put at K1 and selling an OTM call at K2 > K1, profiting from a strong downward move."
+tags: [options, speculation, bearish, risk-reversal]
+---
+
+# Short Combo
+
+**Section**: 2.13 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The short combo (a.k.a. "short risk reversal") amounts to buying an OTM put option with strike K1 and selling an OTM call option with strike K2, where K2 > K1. The trader's outlook is bearish. This is a capital gain strategy.
+
+## Construction
+- Buy 1 OTM put option at strike K1
+- Sell 1 OTM call option at strike K2 (K2 > K1), same expiry
+
+Net debit or credit H (H = D if net debit, H = -C if net credit; K2 > K1)
+
+## Payoff Profile
+f_T = (K1 - S_T)+ - (S_T - K2)+ - H
+
+Breakeven depends on sign of H:
+- S* = K1 - H  (if H > 0, net debit)
+- S* = K2 - H  (if H < 0, net credit)
+- K1 <= S* <= K2  (if H = 0, zero-cost)
+
+- Max profit: P_max = K1 - H  (if stock goes to zero)
+- Max loss: L_max = unlimited  (stock can rise without bound)
+
+## Key Conditions / Signals
+- Strongly bearish outlook
+- Traders often structure as zero-cost (H = 0) by selecting K1 and K2 such that premiums offset
+- Profits from a large downward move; loses if stock rises above K2
+
+## Notes
+The short combo creates a flat zone [K1, K2] where the payoff equals -H. Unlike the short synthetic forward (where K1 = K2 = S0), both strikes are OTM. Unlimited loss potential on the upside due to the short call.

gateway/knowledge/trading/strategies/options/short-guts.md

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+---
+description: "A sideways income strategy selling an ITM call at K1 and an ITM put at K2 > K1, collecting a higher premium than a short straddle but with higher risk and a narrower profit zone."
+tags: [options, income, neutral, guts]
+---
+
+# Short Guts
+
+**Section**: 2.27 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The short guts is a sideways strategy consisting of a short position in an ITM call option with strike K1 and a short position in an ITM put option with strike K2 (K2 > K1). This is a net credit trade. Since both options are ITM, the initial credit is higher than in a short straddle position; the flipside is that the risk is also higher. The trader's outlook is neutral. This is an income strategy. We assume C > K2 - K1.
+
+## Construction
+- Sell 1 ITM call option at strike K1
+- Sell 1 ITM put option at strike K2 (K2 > K1), same expiry
+
+Net credit: C  (assumed C > K2 - K1)
+
+## Payoff Profile
+f_T = -(S_T - K1)+ - (K2 - S_T)+ + C
+
+- Upper breakeven: S*_up = K1 + C
+- Lower breakeven: S*_down = K2 - C
+- Max profit: P_max = C - (K2 - K1)  (if K1 <= S_T <= K2; intrinsic value reduces profit)
+- Max loss: L_max = unlimited  (stock can move far in either direction)
+
+## Key Conditions / Signals
+- Neutral view; expects stock to stay in the range [K1, K2] through expiry
+- The higher credit offsets the reduced maximum profit zone relative to a short straddle
+- High implied volatility environment is ideal for collecting large premium
+
+## Notes
+The assumption C > K2 - K1 prevents risk-free arbitrage. Maximum profit is reduced by the intrinsic spread K2 - K1. The position is short vega and long theta with unlimited directional risk.

gateway/knowledge/trading/strategies/options/short-iron-butterfly.md

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+---
+description: "A neutral volatility strategy combining a bear put spread and a bull call spread around a central ATM strike K2, paying a net debit to profit from a large move away from K2."
+tags: [options, volatility, neutral, butterfly, iron]
+---
+
+# Short Iron Butterfly
+
+**Section**: 2.45 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The "short" iron butterfly is a volatility strategy combining a bear put spread and a bull call spread. It consists of a short OTM put at K1, long ATM put and ATM call at K2, and short OTM call at K3. The strikes are equidistant: K2 - K1 = K3 - K2 = kappa. This is a net debit trade. The trader's outlook is neutral. This is a capital gain strategy.
+
+## Construction
+- Sell 1 OTM put option at strike K1 (lower wing)
+- Buy 1 ATM put option at strike K2 (body)
+- Buy 1 ATM call option at strike K2 (body, same strike as put)
+- Sell 1 OTM call option at strike K3 (upper wing)
+- All same expiry; K2 - K1 = K3 - K2 = kappa (equidistant)
+
+Net debit: D
+
+## Payoff Profile
+f_T = (K2 - S_T)+ + (S_T - K2)+ - (K1 - S_T)+ - (S_T - K3)+ - D
+
+- Upper breakeven: S*_up = K2 + D
+- Lower breakeven: S*_down = K2 - D
+- Max profit: P_max = kappa - D  (if S_T <= K1 or S_T >= K3)
+- Max loss: L_max = D  (if S_T = K2; long straddle at center expires at minimum)
+
+## Key Conditions / Signals
+- Neutral; expects a large move away from K2 in either direction
+- Low implied volatility environment makes the debit cheaper to enter
+- Defined risk on both sides unlike a naked long straddle
+
+## Notes
+The short iron butterfly achieves the same payoff as the long call butterfly or long put butterfly but uses four legs spanning two spreads. The maximum loss is the net debit D, occurring when the stock pins at K2 at expiry.

gateway/knowledge/trading/strategies/options/short-iron-condor.md

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+---
+description: "A neutral volatility strategy combining a bear put spread and a bull call spread with four equidistant strikes, paying a net debit to profit from a large move outside the inner strikes."
+tags: [options, volatility, neutral, condor, iron]
+---
+
+# Short Iron Condor
+
+**Section**: 2.51 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The short iron condor is a volatility strategy combining a bear put spread and a bull call spread. It consists of a short OTM put at K1, a long OTM put at K2, a long OTM call at K3, and a short OTM call at K4. All strikes are equidistant: K4 - K3 = K3 - K2 = K2 - K1 = kappa. This is a net debit trade. The trader's outlook is neutral. This is a capital gain strategy.
+
+## Construction
+- Sell 1 OTM put option at strike K1 (lowest)
+- Buy 1 OTM put option at strike K2 (K2 > K1)
+- Buy 1 OTM call option at strike K3 (K3 > K2)
+- Sell 1 OTM call option at strike K4 (highest, K4 > K3)
+- All same expiry; K2 - K1 = K3 - K2 = K4 - K3 = kappa (equidistant)
+
+Net debit: D
+
+## Payoff Profile
+f_T = (K2 - S_T)+ + (S_T - K3)+ - (K1 - S_T)+ - (S_T - K4)+ - D
+
+- Upper breakeven: S*_up = K3 + D
+- Lower breakeven: S*_down = K2 - D
+- Max profit: P_max = kappa - D  (if S_T <= K1 or S_T >= K4)
+- Max loss: L_max = D  (if K2 <= S_T <= K3; inner spreads expire worthless)
+
+## Key Conditions / Signals
+- Neutral; expects stock to move significantly outside the [K2, K3] range
+- Low implied volatility makes the net debit cheaper to enter
+- Defined risk on both sides with defined maximum profit
+
+## Notes
+The short iron condor is the reverse of the long iron condor. A net debit is paid and the strategy profits from large moves in either direction. The maximum loss D occurs if the stock stays between K2 and K3; maximum profit kappa - D is achieved outside [K1, K4].

gateway/knowledge/trading/strategies/options/short-put-butterfly.md

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+---
+description: "A neutral net credit strategy selling an ITM put at K1, buying two ATM puts at K2, and selling an OTM put at K3, profiting from a large move away from K2."
+tags: [options, volatility, neutral, butterfly]
+---
+
+# Short Put Butterfly
+
+**Section**: 2.43 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The short put butterfly is a volatility strategy consisting of a short ITM put at K1, a long position in two ATM puts at K2, and a short OTM put at K3. The strikes are equidistant: K2 - K3 = K1 - K2 = kappa. This is a net credit trade. In this sense it is an income strategy. However, the potential reward is sizably smaller than with a short straddle or short strangle (albeit with lower risk). The trader's outlook is neutral.
+
+## Construction
+- Sell 1 put option at strike K1 (ITM, upper wing, K1 > K2)
+- Buy 2 put options at strike K2 (ATM, body)
+- Sell 1 put option at strike K3 (OTM, lower wing, K3 < K2)
+- All same expiry; K1 - K2 = K2 - K3 = kappa (equidistant)
+
+Net credit: C
+
+## Payoff Profile
+f_T = 2 × (K2 - S_T)+ - (K1 - S_T)+ - (K3 - S_T)+ + C
+
+- Lower breakeven: S*_down = K3 + C
+- Upper breakeven: S*_up = K1 - C
+- Max profit: P_max = C  (if S_T >= K1 or S_T <= K3)
+- Max loss: L_max = kappa - C  (if S_T = K2 at expiry)
+
+## Key Conditions / Signals
+- Neutral; expects stock to move significantly away from K2 by expiry
+- High implied volatility environment; collect larger credit upfront
+- Lower risk than a short straddle or strangle but also lower reward
+
+## Notes
+The short put butterfly is the reverse of the long put butterfly. Credit is collected upfront and profit is achieved if the stock moves far enough from K2. The maximum loss is bounded by the wing width kappa minus the credit received.

gateway/knowledge/trading/strategies/options/short-put-condor.md

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+---
+description: "A neutral volatility strategy selling an OTM put at K1 and ITM put at K4 while buying puts at K2 and K3, collecting credit and profiting from a large move outside [K1, K4]."
+tags: [options, volatility, neutral, condor]
+---
+
+# Short Put Condor
+
+**Section**: 2.49 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The short put condor is a volatility strategy consisting of a short OTM put at K1, a long OTM put at K2, a long ITM put at K3, and a short ITM put at K4. All strikes are equidistant: K4 - K3 = K3 - K2 = K2 - K1 = kappa. This is a relatively low net credit trade. As with a short put butterfly, the potential reward is sizably smaller than with a short straddle or short strangle (albeit with lower risk). So this is a capital gain (rather than income) strategy. The trader's outlook is neutral.
+
+## Construction
+- Sell 1 put option at strike K1 (OTM, lowest)
+- Buy 1 put option at strike K2 (OTM, K2 > K1)
+- Buy 1 put option at strike K3 (ITM, K3 > K2)
+- Sell 1 put option at strike K4 (ITM, highest, K4 > K3)
+- All same expiry; K2 - K1 = K3 - K2 = K4 - K3 = kappa (equidistant)
+
+Net credit: C
+
+## Payoff Profile
+f_T = (K2 - S_T)+ + (K3 - S_T)+ - (K1 - S_T)+ - (K4 - S_T)+ + C
+
+- Upper breakeven: S*_up = K4 - C
+- Lower breakeven: S*_down = K1 + C
+- Max profit: P_max = C  (if S_T <= K1 or S_T >= K4)
+- Max loss: L_max = kappa - C  (if K2 <= S_T <= K3 at expiry)
+
+## Key Conditions / Signals
+- Neutral; expects stock to move significantly outside the [K1, K4] range
+- High implied volatility environment; collect larger credit upfront
+- Defined risk on both sides, making it safer than a short straddle
+
+## Notes
+The short put condor has the same payoff as the short call condor (by put-call parity). Net credit is collected and the strategy profits from large moves in either direction. Maximum loss kappa - C occurs if the stock stays in the middle zone [K2, K3].

gateway/knowledge/trading/strategies/options/short-put-synthetic-straddle.md

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+---
+description: "A sideways strategy shorting stock and selling two ATM puts at strike K, replicating a short straddle by replacing the short call with a synthetic short call."
+tags: [options, income, neutral, synthetic, straddle]
+---
+
+# Short Put Synthetic Straddle
+
+**Section**: 2.31 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The short put synthetic straddle (the same as a short straddle with the call replaced by a synthetic call) amounts to shorting stock and selling two ATM (or nearest OTM) put options with strike K. The trader's outlook is neutral. This is a capital gain strategy. We assume S0 >= K.
+
+## Construction
+- Short 1 share of stock at S0
+- Sell 2 ATM put options at strike K, same expiry
+
+Net credit: C
+
+## Payoff Profile
+f_T = S0 - S_T - 2 × (K - S_T)+ + C
+
+- Upper breakeven: S*_up = S0 + C
+- Lower breakeven: S*_down = 2K - S0 - C
+- Max profit: P_max = S0 - K + C  (at S_T = K)
+- Max loss: L_max = unlimited  (stock can fall without bound; short 2 puts + short stock)
+
+## Key Conditions / Signals
+- Neutral view; expects stock to stay near K through expiry
+- S0 >= K (stock at or above the put strike)
+- High implied volatility makes the collected credit from the two short puts larger
+
+## Notes
+Unlimited loss on the downside due to the two short puts combined with the short stock position. The short stock provides partial offset against falling prices but is insufficient beyond the breakeven. Active management or stop-losses are essential.

gateway/knowledge/trading/strategies/options/short-straddle.md

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+---
+description: "A sideways income strategy selling an ATM call and an ATM put at the same strike K, collecting premium when the stock stays near K."
+tags: [options, income, neutral, straddle]
+---
+
+# Short Straddle
+
+**Section**: 2.25 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The short straddle is a sideways strategy consisting of a short position in an ATM call option and a short position in an ATM put option with the same strike K. This is a net credit trade. The trader's outlook is neutral. This is an income strategy that profits if the stock remains near K until expiry.
+
+## Construction
+- Sell 1 ATM call option at strike K
+- Sell 1 ATM put option at strike K, same expiry
+
+Net credit: C
+
+## Payoff Profile
+f_T = -(S_T - K)+ - (K - S_T)+ + C
+
+- Upper breakeven: S*_up = K + C
+- Lower breakeven: S*_down = K - C
+- Max profit: P_max = C  (if S_T = K at expiry; both options expire worthless)
+- Max loss: L_max = unlimited  (stock can move far in either direction)
+
+## Key Conditions / Signals
+- Neutral view; expects stock to remain very close to K through expiry
+- High implied volatility environment makes the collected credit larger
+- Ideal when volatility is expected to contract (sell elevated IV, profit from IV crush)
+
+## Notes
+Unlimited risk in both directions. The position is short vega and long theta. A sharp move in either direction can result in catastrophic losses. Active management (delta hedging or stop-losses) is essential.

gateway/knowledge/trading/strategies/options/short-strangle.md

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+---
+description: "A sideways income strategy selling an OTM call at K1 and an OTM put at K2 < K1, collecting premium with a wider profit zone than a short straddle but lower credit."
+tags: [options, income, neutral, strangle]
+---
+
+# Short Strangle
+
+**Section**: 2.26 | **Asset Class**: Options | **Type**: Income
+
+## Overview
+The short strangle is a sideways strategy consisting of a short position in an OTM call option with strike K1 and a short position in an OTM put option with strike K2 (K2 < K1). This is a net credit trade. Since both options are OTM, this strategy is less risky than a short straddle position; the flipside is that the initial credit is also lower. The trader's outlook is neutral. This is an income strategy.
+
+## Construction
+- Sell 1 OTM call option at strike K1
+- Sell 1 OTM put option at strike K2 (K2 < K1), same expiry
+
+Net credit: C
+
+## Payoff Profile
+f_T = -(S_T - K1)+ - (K2 - S_T)+ + C
+
+- Upper breakeven: S*_up = K1 + C
+- Lower breakeven: S*_down = K2 - C
+- Max profit: P_max = C  (if K2 <= S_T <= K1 at expiry; both options expire worthless)
+- Max loss: L_max = unlimited  (stock can move far in either direction)
+
+## Key Conditions / Signals
+- Neutral view; expects stock to remain between K2 and K1 through expiry
+- High implied volatility environment makes the collected credit larger
+- Wider profit zone than a short straddle, but smaller credit collected
+
+## Notes
+Unlimited risk in both directions once the stock moves outside [K2, K1]. The position is short vega and long theta. Less risky than the short straddle but still requires active management for large moves.

gateway/knowledge/trading/strategies/options/short-synthetic-forward.md

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+---
+description: "A bearish capital-gain strategy buying an ATM put and selling an ATM call at the same strike K = S0, replicating a short forward contract on the underlying."
+tags: [options, speculation, bearish, synthetic]
+---
+
+# Short Synthetic Forward
+
+**Section**: 2.11 | **Asset Class**: Options | **Type**: Speculation
+
+## Overview
+The short synthetic forward amounts to buying an ATM put option and selling an ATM call option with the same strike K = S0. This can be a net debit or net credit trade; typically |H| << S0. The trader's outlook is bearish: this strategy mimics a short stock or futures position and replicates a short forward contract with delivery price K and the same maturity as the options. This is a capital gain strategy.
+
+## Construction
+- Buy 1 ATM put option at strike K = S0
+- Sell 1 ATM call option at strike K = S0, same expiry
+
+Net debit or credit H (H = D for net debit trade, H = -C for net credit trade)
+
+## Payoff Profile
+f_T = (K - S_T)+ - (S_T - K)+ - H = K - S_T - H
+
+- Breakeven: S* = K - H
+- Max profit: P_max = K - H  (if stock goes to zero)
+- Max loss: L_max = unlimited  (stock can rise without bound)
+
+## Key Conditions / Signals
+- Strongly bearish outlook seeking full participation in downside
+- Useful when short-selling the stock directly is restricted or costly
+- Typically near-zero net premium (H is small relative to S0)
+
+## Notes
+The payoff is linear in S_T — identical to short stock (minus K - H). The upside is not limited; the position loses as the stock rises above K, just like a short stock position.

gateway/knowledge/trading/strategies/options/strap.md

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+---
+description: "A bullish volatility strategy buying two ATM calls and one ATM put at strike K, profiting more from an upward move than a downward move of equal magnitude."
+tags: [options, volatility, bullish, strap]
+---
+
+# Strap
+
+**Section**: 2.34 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The strap is a volatility strategy consisting of a long position in two ATM call options and a long position in one ATM put option with strike K. This is a net debit trade. The trader's outlook is bullish (skewed toward upside). This is a capital gain strategy that profits from a large move in either direction but gains more from an upward move.
+
+## Construction
+- Buy 2 ATM call options at strike K
+- Buy 1 ATM put option at strike K, same expiry
+
+Net debit: D
+
+## Payoff Profile
+f_T = 2 × (S_T - K)+ + (K - S_T)+ - D
+
+- Upper breakeven: S*_up = K + D/2
+- Lower breakeven: S*_down = K - D
+- Max profit: P_max = unlimited  (especially strong on upside due to 2 calls)
+- Max loss: L_max = D  (if S_T = K at expiry)
+
+## Key Conditions / Signals
+- Bullish but uncertain of direction; expects a large move with upside bias
+- Low implied volatility environment is ideal (cheaper debit to enter)
+- The upper breakeven (D/2 above K) is closer to K than the lower breakeven (D below K)
+
+## Notes
+The strap is a modified straddle with bullish skew: two calls vs. one put. The upside potential is doubled relative to the downside (per unit of move). Maximum loss is capped at the net debit D.

gateway/knowledge/trading/strategies/options/strip.md

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+---
+description: "A bearish volatility strategy buying one ATM call and two ATM puts at strike K, profiting more from a downward move than an upward move of equal magnitude."
+tags: [options, volatility, bearish, strip]
+---
+
+# Strip
+
+**Section**: 2.35 | **Asset Class**: Options | **Type**: Volatility
+
+## Overview
+The strip is a volatility strategy consisting of a long position in one ATM call option and a long position in two ATM put options with strike K. This is a net debit trade. The trader's outlook is bearish (skewed toward downside). This is a capital gain strategy that profits from a large move in either direction but gains more from a downward move.
+
+## Construction
+- Buy 1 ATM call option at strike K
+- Buy 2 ATM put options at strike K, same expiry
+
+Net debit: D
+
+## Payoff Profile
+f_T = (S_T - K)+ + 2 × (K - S_T)+ - D
+
+- Upper breakeven: S*_up = K + D
+- Lower breakeven: S*_down = K - D/2
+- Max profit: P_max = unlimited  (especially strong on downside due to 2 puts)
+- Max loss: L_max = D  (if S_T = K at expiry)
+
+## Key Conditions / Signals
+- Bearish but uncertain of direction; expects a large move with downside bias
+- Low implied volatility environment is ideal (cheaper debit to enter)
+- The lower breakeven (D/2 below K) is closer to K than the upper breakeven (D above K)
+
+## Notes
+The strip is a modified straddle with bearish skew: two puts vs. one call. The downside potential is doubled relative to the upside (per unit of move). Maximum loss is capped at the net debit D.