Using Delta-Specific Volatility to Infer Option Strikes

Summary

The document addresses which implied volatility to use when converting a quoted option delta into a strike. Its guidance is to use the volatility associated with that particular delta, together with the other inputs required by the option-pricing relationship, such as the underlying price, time to expiry, interest rate, and dividend yield.

At-the-money volatility is appropriate when inferring the at-the-money strike. For other deltas, the expiry’s volatility smile or smirk means implied volatility varies across strikes, so applying the ATM value across the curve can produce an inconsistent strike. The answer is brief and does not give a numerical example, specify a pricing convention, or explain an iterative calibration procedure.

Key ideas

• Use the implied volatility corresponding to the target delta when inferring its strike.\nATM volatility is suitable for deriving the at-the-money strike.\nA volatility smile or smirk means one expiry can have different implied volatilities across strikes.\nStrike inference also depends on the underlying, expiry, rates, and dividend yield.

Tags

# What vol to use when implying strike from delta?


# What vol to use when implying strike from delta?












I have a set of implied vols in delta space and want to derive for each delta the corresponding strike. I understand the procedure, but I am not sure what implied vol I should use, whether this has to be the ATM vol or the vol for the fitted vol for that specific delta.

Thanks!

## Answer by Hui (score 2)

https://quant.stackexchange.com/a/40397

The answer is vol for specific delta.You can use ATM vol to back out ATM strike. Because Vols of strikes on the same expiry is a smile(smirk), not a flat line, you have to use different vols to back out corresponding strikes based on delta and other given option variables(underlying price, vol, t, r, q).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.