What We Can Learn from Pricing 139,879 Individual Stock Options

Abstract

It has long been obvious that stock volatility is not a constant knowable parameter, as the original Black–Scholes model assumed, but no single extension to stochastic time-varying volatility has replaced it. The GARCH family of volatility models has the highly desirable feature that variance is a direct function of returns, so there is still only one source of risk, and volatility can be estimated easily from observed data. There are still unsettled issues in this framework, however, including which GARCH model to use, whether an asymmetry term should be included, and whether return shocks should be assumed to come from a normal distribution or some fatter-tailed alternative. In this article, Stentoft runs a horse race among GARCH-type models using the 30 stocks in the Dow Jones Industrial Average. An interesting innovation is to use the relatively new theory of model confidence sets in the testing procedure. The winner is NGARCH with normal inverse Gaussian errors.