Why Higher Volatility Widens Fixed-Delta Option Strikes

Summary

The note addresses how the strike locations for a fixed-delta option skew measure change when implied volatility rises. The measure compares the implied volatilities of a 25-delta put and call, with their separation from the at-the-money region expressed relative to a 50-delta option. The question is whether higher volatility makes those selected strikes closer to the money or farther away.

The explanation relies on the direction of delta across out-of-the-money strikes: delta becomes smaller as a strike moves farther out of the money. Raising volatility increases the absolute delta at a given out-of-the-money strike, so reaching the target 25-delta value requires moving farther out of the money. This widens the strike range used in the measure. The response is a concise qualitative clarification; it does not derive the relationship from an option pricing model or discuss effects of rates, dividends, or market conventions.

Key ideas

• An out-of-the-money option’s delta generally falls as its strike moves farther from the money.
• At a fixed strike, higher implied volatility increases the absolute delta of an out-of-the-money option.
• To return to a target 25-delta level after volatility rises, the strike must move farther out of the money.
• A fixed-delta skew measure therefore examines a wider strike range when volatility increases.

Tags

# Delta Skew Measure as volatility changes


# Delta Skew Measure as volatility changes












I'm reading Trading Volatility (Colin Bennett) and there's a phrase regarding delta skew measure on p. 208 that I don't quite understand:

> An example of skew measured by delta is [25 delta put - 25 delta call] / 50 delta. As this measure WIDENS the strikes examined as vol rises, in addition to normalizing (i.e., dividing) by the level of Volatility, it is a "pure" measure of skew.

I have a problem with the word "widens". As I understand for OTM options if you increase the implied vol the absolute delta will rise. So if vol has rised as written above, then wouldn't a 25 call/put has a tighter strike range? (Lower strike for the call and higher strike for the put). Because for the same delta 25, since vol is higher, the strike does not need to work as much in our favor so to speak. Therefore, wouldn't it be that when vol rises, the strike range of the skew is tighter and when vol decreases, the strike range will be wider?

I feel like my reasoning is in reverse somehow but I just can't put a finger on it.

Thanks for any help.

## Answer by msitt (score 1)

https://quant.stackexchange.com/a/50722

The important thing here is that delta gets smaller as you get further out of the money.

You are correct that the delta of the option will increase if vol increases. So to find the new 25 delta strikes, you will need to go further out of the money, i.e. wider strike range.

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