# Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff;

Could you ^please help me !

## 1 Answer

A butterfly in general has a payoff of the form \begin{align*} (X_T-K_c)^+ + (K_p-X_T)^+-(X_T-K_{atm})^+-(K_{atm}-X_T)^+, \end{align*} where $X_T$ is the asset value at maturity $T$, while $K_c$, $K_p$, and $K_{atm}$ are strike levels.

• What are $K_{p}$, $K_{atm}$, $K_{c}$ ? Actually my function take a single Strike which is the strike for call and put, is it possible to define Butterfly in function of the two payoff I have already (call and put) with one strike ? – Sino Feb 11 '16 at 20:15
• A butterfly always involves three strikes, and is in the form above. It is possible to take two strikes by assuming that $K_{atm} = \frac{K_c+K_p}{2}$, but that is not the butterfly in general. – Gordon Feb 11 '16 at 20:28