SHORT CALL BUTTERFLY

This is a volatility Strategy consisting of a short position in an ITM call option with a Strike price K1, a long position in two ATM call options with a strike price K2, and a short position in an OTM call option with a strike price K3. The strikes are equidistant: K3 − K2 = K2 − K1 = κ. This is a net credit trade. In this sense, this is an income strategy. However, the potential reward is sizably smaller than with a short straddle or a short strangle (albeit with a lower risk). The trader’s outlook is neutral. We have:

fT = 2 × (ST − K2)⁺ − (ST − K1)⁺ − (ST − K3)⁺ + C

S∗up = K3 − C

S∗down = K1 + C

Pmax = C

Disclaimer: A call option is a right (but not an obligation) to buy a stock at the maturity time T for the strike price k agreed on at time t = 0.

The claim for the call option 

fcall(ST , k) = (ST − k)⁺                                    Here (x)⁺ = x

if x > 0 and (x)⁺