Skip to content
All library documents

Why Gamma Falls for Deep In-the-Money Options

Article Quant Q&A · Author: julesc
Read the original

Summary

The document explains why an option’s gamma tends to decline as it moves far in or far out of the money. It corrects the idea that gamma measures market demand: gamma is a mathematical measure of how quickly delta changes as the underlying price moves, and it reflects the option’s convexity.

For a deep in-the-money option, delta approaches a near-constant value because the option behaves increasingly like the underlying asset. With little change in delta, gamma approaches zero. The discussion also suggests why traders seeking optionality may have less interest in such contracts, while traders wanting steady directional exposure can use the underlying. This is a conceptual explanation rather than an empirical study; it does not quantify how quickly gamma falls or address differences across pricing models, maturities, or market conditions.

Key ideas

  • Gamma measures the rate of change in delta, not demand for an option.
  • An option’s gamma reflects the convexity of its payoff with respect to the underlying price.
  • Deep in-the-money options increasingly behave like the underlying, so their delta changes little.
  • When delta is nearly constant, gamma approaches zero.
  • Traders seeking optionality may prefer contracts whose delta remains more responsive to price changes.

Tags

OptionsDerivatives pricingVolatility
Full text
# why gamma decreases when option is deep in the money?


# why gamma decreases when option is deep in the money?












Gamma decreases when a call option goes either deeper in, or deeper out of the money. That is due the demand for the call option. I can imagine the demand for the option would decrease as it goes deeper out of the money, but I would expect the demand for the option should increase as it goes deeper in the money because it would make more profit for the holder of the option. Why is this not true? In other words, why does the demand for the option decrease despite the fact that a deep in the money option is more profitable?

## Answer by Ezy (score 3)

https://quant.stackexchange.com/a/43439

Gamma is not linked to the supply/demand for an option. It is a purely analytic effect that reflects the convexity of the product.

## Answer by AlRacoon (score 3)

https://quant.stackexchange.com/a/43440

Gamma is the speed at which Delta changes. When options are deep in the money, they trade like the underlying. In other words the Delta doesn't change and therefore Gamma is zero. In mathematical terms, the second derivative which measures the rate of change of the first derivative, is zero if the first derivative is a constant.

With respect to demand for the option, if it trades like the underlying, I would expect that the traders of options that are using it for the optionality would not be in the market for those options. For those that are looking for constant Delta, the could just buy the underlying and adjust for any implied leverage in the option by just taking a leveraged position.

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.