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Ideal expiry price for a 35/37.5/40 butterfly

Question

You go long a butterfly built from options struck at 3535 and 4040 (the wings) and 37.537.5 (the body). At expiry, what stock price would you most like to see?

Short answer

37.537.5. A long butterfly is long one option at each wing and short two at the body, so its payoff is a tent that is zero outside [35,40][35,40] and peaks at the middle strike.

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