---
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.