How Volatility Changes Gamma Across Moneyness

Summary

The document gives an intuition for how an increase in implied volatility can affect the gamma of European vanilla options. Gamma measures how quickly delta changes as the underlying price moves. For options near the money, higher volatility makes nearby strikes behave more similarly, so delta changes less sharply with spot and gamma can decline. The explanation complements the Black–Scholes gamma formula by describing the effect through moneyness and delta behavior.

The effect can differ for far out-of-the-money options. At low volatility these options may have almost no delta, and small moves toward the strike may still leave them with little gamma. Higher volatility makes them behave as though they are closer to the money, which can increase gamma. These are qualitative intuitions rather than a full analysis: the document does not specify how gamma varies across all strikes, maturities, or volatility levels, and the effect depends on the option’s position relative to the money.

Key ideas

• Gamma describes how quickly an option’s delta changes as the underlying price moves.
• For options near the money, higher volatility can make nearby strikes more alike and reduce gamma.
• For far out-of-the-money options, higher volatility can increase gamma by making them behave more like near-the-money options.
• The volatility effect on gamma depends on moneyness.

Tags

# European vanilla call/put option, when volatility increases, how will gamma changes?


# European vanilla call/put option, when volatility increases, how will gamma changes?












according to the BS formula, $\gamma = \frac{N'(d_1)}{S_0\sigma\sqrt{T}}$, gamma will decrease when volatility increase.

How does it intuitively make sense? rather than from the formula.

## Answer by user15229 (score 2)

https://quant.stackexchange.com/a/16405

For ATMish options, as vol goes higher, the option looks even more ATM. That is, at higher vol, the difference between a 99% strike option and a 100% strike option is less pronounced than if vol were low; hence your deltas won't change as fast as spot moves and thus, less gamma.

For far OTM options, its the opposite. They would have very little delta at low vol, and remain dead even as you start to move a little closer to them, so have little gamma. However as vol picks up, its like the options are less OTM, so start to have some more gamma.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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