Where should the butterfly expire?

Quantitative Finance Level 1

You are long a 5-10-15 butterfly. On which of the following expiration price(s) will you make the most money?

5 or 15 7.5 or 12.5 2.5 or 17.5 10

1 solution

Chew-Seong Cheong
Feb 19, 2015

A long butterfly spread strategy is to long (buy) one lower striking in-the-money call, short (sell/write) two at-the-money calls and long another higher striking out-of-the-money call.

Maximum profit for the long butterfly spread is attained when the underlying stock price remains unchanged (as that of the at-the-money calls) at expiration. At this price, only the lower striking call expires in the money ( see more here ).

In general, you want the options to expire at your short strike, and away from your long strike.

The equivalent mathematical statement is that the (local) maximum of $\sum C_i \max ( 0, X_i- S) + P_i \max ( 0, S - X_i )$ occurs ... (fill in the blank).

Calvin Lin Staff - 6 years, 3 months ago

Where should the butterfly expire?

1 solution

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