---
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.