Tim Olson
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description, tags
| description | tags | |||||
|---|---|---|---|---|---|---|
| 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. |
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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).