BROWSE

Gamma

What is 'Gamma'

Gamma is the rate of change in an option's delta per 1-point move in the underlying asset's price. Gamma is an important measure of the convexity of a derivative's value, in relation to the underlying. A delta hedge strategy seeks to reduce gamma in order to maintain a hedge over a wider price range. A consequence of reducing gamma, however, is that alpha will also be reduced.

Explaining 'Gamma'

Gamma Behavior

Since an option's delta measure is only valid for short period of time, gamma gives portfolio managers, traders and individual investors a more precise picture of how the option's delta will change over time as the underlying price changes. As an analogy to physics, the delta of an option is its "speed," while the gamma of an option is its "acceleration." Gamma decreases, approaching zero, as an option gets deeper "in-the-money," as delta approaches one. Gamma also approaches zero the deeper an option gets "out-of-the-money." Gamma is at its highest approximately "at-the-money."


Further Reading


The gamma function inequalities of Gurland and Gautschi
www.tandfonline.com [PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

Bayesian Inference in Parameters of Gamma Distribution with Multiple Change Points <span style=[J]' src='/thumbnails/?img=http%3A%2F%2Fen.cnki.com.cn%2FArticle_en%2FCJFDTotal-HNDX903.024.htm' />Bayesian Inference in Parameters of Gamma Distribution with Multiple Change Points [J]
en.cnki.com.cn [[J]' href='https:/api.miniature.io/pdf?url=en.cnki.com.cn%2FArticle_en%2FCJFDTotal-HNDX903.024.htm'>PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

Risk Measure of FX Options Based on Delta-Gamma-Theta Model <span style=[J]' src='/thumbnails/?img=http%3A%2F%2Fen.cnki.com.cn%2FArticle_en%2FCJFDTotal-XTLL200507008.htm' />Risk Measure of FX Options Based on Delta-Gamma-Theta Model [J]
en.cnki.com.cn [[J]' href='https:/api.miniature.io/pdf?url=en.cnki.com.cn%2FArticle_en%2FCJFDTotal-XTLL200507008.htm'>PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

On American options under the Variance Gamma processOn American options under the Variance Gamma process
www.tandfonline.com [PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

Minimum variance unblased estimation in the gamma distributionMinimum variance unblased estimation in the gamma distribution
www.tandfonline.com [PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

Algorithmic Hessians and the fast computation of cross-gamma riskAlgorithmic Hessians and the fast computation of cross-gamma risk
www.tandfonline.com [PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

Options and the gamma knifeOptions and the gamma knife
jod.pm-research.com [PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

REDD+ Readiness progress across countries: time for reconsiderationREDD+ Readiness progress across countries: time for reconsideration
www.tandfonline.com [PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

The gamma-exponentiated exponential distributionThe gamma-exponentiated exponential distribution
www.tandfonline.com [PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …

Ruin probabilities in classical risk models with gamma claimsRuin probabilities in classical risk models with gamma claims
www.tandfonline.com [PDF]
… CrossRef citations to date. Altmetric. Original Articles. The gamma function inequalities of Gurland and Gautschi. Thomas Erber Illinois Institute of Technology … Original Articles. The gamma function inequalities of Gurland and Gautschi …



Q&A About Gamma


Are there any other special cases of this family of distributions?

Yes, they include exponential, Erlang, chi-square distributions.

What is the rate of change in an option's delta per 1-point move in the underlying asset's price?

Gamma is the rate of change in an option's delta per 1-point move in the underlying asset's price.

Why would you want to reduce gamma?

Gamma gives portfolio managers, traders and individual investors more precise information about how options' deltas will change over time as the underlying price changes. As an analogy, think about physics; delta is like speed while gamma is like acceleration. The closer your car gets to zero miles per hour (delta), or zero dollars (gamma), the slower it goes (theta) and its acceleration decreases (vega). When your car moves at high speeds, its acceleration increases substantially but then drops off again as it slows down toward zero miles per hour or zero dollars. Similarly, when an option approaches deep "in-the-money" status, its value accelerates quickly but then decelerates as it becomes deeper "out-of-the-money." This pattern repeats itself for all options with different strike prices and expiration dates. In other words, if you know how fast something goes at one point on its path and how quickly it slows down later on along that path, you can estimate what speed it will have at any point along that path between those two points by extrapolating from those two known points using simple math functions such as linear interpolation

How does gamma affect hedge strategies?

A delta hedge strategy seeks to reduce gamma so that it can maintain a hedge over a wider range of prices.

What does gamma measure?

Gamma measures how much an option changes as a result of a small change in the underlying asset.

Is there another parameterization for this function besides k i ?

Yes, it includes i k i and i  i .

What happens when you try to reduce gamma?

Alpha will also be reduced.

What does it mean to have an expectation greater than zero but less than one?

This means that there will be more negative values than positive values in your data set.

How can you determine if something is a maximum entropy probability distribution?

You need to know what its expectation and variance are.

What is the gamma distribution?

The gamma distribution is a two-parameter family of continuous probability distributions.

What does it mean to be a maximum entropy probability distribution?

It means that this is a random variable with fixed expectation and variance, and maximum entropy.

What are the parameters for the gamma distribution?

The parameters for the gamma distribution are

Why would someone use one over another parameterization?

Econometrics uses k i , while statistics uses both forms equally often.

If you take the logarithm of both sides of an equation involving these three functions what do you get?

You get .