Assuming we have a correct final value of realized volatility, how would one calculate the expected return of a strangle?

Given that a strangle is a bet on volatility it seems that it should be possible to estimate the expected return of a strangle given the difference between the implied volatility when entering the strangle and the realized volatility at expiration.

For simplicity let's assume a symmetric strangle that sell the same number of contracts for puts and calls. However given skew the IV of the puts and calls will be different. It seems naive to simply average them to get the IV of the strangle. If that is the case it also seems then that taking the combined position


Would be the expected profit. Intuition tells me this might work better for an at the money straddle, but strangles seem more path dependent.



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