---
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).