Gamma Pricing Model
What Is the Gamma Pricing Model?
The gamma pricing model is an equation for deciding the fair market value of a European- style options contract when the price movement on the underlying asset doesn't follow a normal distribution. The Gamma model is expected rather to price options where the underlying asset has a distribution that is long-tailed ("skewed"). This, for example, is the case for a log-normal distribution, where emotional market moves to the downside happen with greater frequency than would be anticipated by a normal distribution of returns relative to large upside swings.
The gamma model is one alternative for pricing options other than the original Black-Scholes model, which requires the assumption of a normal distribution. Others incorporate the binomial tree, trinomial tree, and [lattice models](/cross section model), among others.
Understanding the Gamma Pricing Model
While the Black-Scholes option pricing model is the best known in the financial world, it doesn't really give accurate pricing results under all circumstances. Specifically, the Black-Scholes model expects that the underlying instrument has returns that are normally distributed in a symmetrical way.
Subsequently, the Black-Scholes model will keep an eye on misprice options on instruments that don't trade in light of a normal distribution, specifically, underestimating downside puts. What's more, these errors lead traders to one or the other over-or under-hedge their positions on the off chance that they try to involve options as insurance, or then again on the off chance that they are trading options to capture the level of volatility in an asset.
Numerous alternative options pricing methods have been developed determined to give more accurate pricing to certifiable applications, for example, the Gamma Pricing Model. Generally talking, the Gamma Pricing Model utilizes the option's gamma, which is how much fast the delta changes with respect to small changes in the underlying asset's price (where the delta is the change in option price given a change in the price of the underlying asset).
Gamma and Volatility Skew
By zeroing in on the gamma, which is basically the shape, or acceleration, of the options price as the underlying asset moves, investors can account for the downside volatility skew (otherwise called the volatility "smile") coming about because of the lack of a normal distribution. To be sure, stocks' price returns will generally have a far greater frequency of large downside moves than upside swings. Besides, stock prices are limited to the downside by zero, though they have unlimited upside potential.
Most investors in stocks (and different assets) will generally hold long positions and use options as a hedge for downside protection. This drives more interest to buy lower strike options than higher ones.
The gamma model changes take into consideration a more accurate representation of the distribution of asset prices and, subsequently, a better impression of options' true fair values.
Features
- The model is utilized to price options on assets that have a distribution that is either fat-followed or skewed, like the log-normal distribution.
- The model uses an option's gamma or arch to changes in its price sensitivity as the underlying asset moves.
- The gamma model for pricing options is utilized to all the more accurately address the distribution of asset prices that are asymmetric and is subsequently a better impression of an option's fair value.
