Tim Olson
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35 lines
1.5 KiB
Markdown
35 lines
1.5 KiB
Markdown
---
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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."
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tags: [options, volatility, neutral, synthetic, straddle]
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---
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# Long Put Synthetic Straddle
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**Section**: 2.29 | **Asset Class**: Options | **Type**: Volatility
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## Overview
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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.
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## Construction
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- Buy 1 share of stock at S0
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- Buy 2 ATM put options at strike K, same expiry
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Net debit: D (assumed D > K - S0)
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## Payoff Profile
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f_T = S_T - S0 + 2 × (K - S_T)+ - D
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- Upper breakeven: S*_up = S0 + D
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- Lower breakeven: S*_down = 2K - S0 - D
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- Max profit: P_max = unlimited (large move in either direction)
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- Max loss: L_max = D - (K - S0) (at S_T = K; intrinsic offset reduces loss)
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## Key Conditions / Signals
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- Neutral view; expects a large move in either direction
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- S0 <= K (stock at or below the put strike)
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- D > K - S0 prevents arbitrage
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- Useful when calls are expensive relative to puts (use puts to synthesize the straddle)
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## Notes
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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).
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