Interpreting Claims That Option Gamma Becomes Gaussian
Summary
The note discusses what an informal claim that option gamma becomes more Gaussian might mean. One interpretation is that a plot of gamma against stock price takes on a broad, roughly symmetric bell shape at longer maturities, while short-dated gamma can look sharply peaked. In this usage, Gaussian is a visual analogy rather than a precise claim that the curve follows a normal distribution.
It also connects gamma to delta: gamma measures how quickly delta changes as the underlying price moves. At expiry, a call’s delta approaches a step from zero to one around the strike, and gamma concentrates around that transition. The answers caution that an actual gamma curve need not be symmetric or match a textbook normal curve. They also give inconsistent intuition about the effect of time: one answer associates a step-like delta with less time to expiry or lower volatility, so the phrase should not be treated as a clear general rule without specifying the option and conditions.
Key ideas
- Gaussian may be used informally to describe a bell-shaped gamma curve.
- Gamma measures the rate at which option delta changes with the underlying price.
- As a call approaches expiry, its delta tends toward a step around the strike and gamma becomes concentrated there.
- An option’s gamma curve need not be symmetric or match a normal distribution.
- Claims about maturity and Gaussian shape require qualification because the explanations are imprecise.
Tags
Full text
# What does it mean for something to become more gaussian? # What does it mean for something to become more gaussian? I was reading something in which the author said: "the longer the maturity, the more and more gaussian the gamma of your option is". What exactly is the author trying to say in non-math terms and what does it mean to become more and more gaussian? ## Answer by nbbo2 (score 6) https://quant.stackexchange.com/a/53704 This statement is both unclear and somewhat incorrect. To be more understandable the author should have said "as the option maturity becomes longer, the curve of Gamma vs stock price takes on more and more a broad, symmetrical bell shape". So he is using the fancy word Gaussian as a synonym for Bell Shaped, not as a precise math term. For short term options he could have said "on the other hand when maturity is short the curve of Gamma vs S looks like a sharp Spike or an Upside Down Icicle". However, if you look at this graph, for example link you will see that the gamma curve is not truly symmetric and differs visibly from the Gaussian curve shown in math textbooks link2. So the statement is imprecise at best. ## Answer by Andreas (score 2) https://quant.stackexchange.com/a/53697 In short: It's equivalent to saying the Gamma, in your case, becomes more normally distributed / resembles a normal distribution, which comes with a set of well known properties, such as being symmetrical and having a mean of $\mu$ and a standard deviation of $\sigma$. Explanation: Gamma, being the first derivative, indicates the rate of change of the options Delta. The Gamma becoming more and more Gaussian is a result of the Delta moving closer to a step function*. This is typically a sign of lower uncertainty, due to less time until maturity and/or lower volatility. * A function that is zero when $S \leq X$ and then "jumps" up to one for $S>X$ for a call option at maturity.
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.