6 - Stochastic volatility and option pricing

Abstract

This chapter reviews the present literature on applications of stochastic volatility (SV) models in pricing options. It includes discussions on modeling of SV in both discrete time and continuous time and modeling of SV with jumps, option pricing under SV and implications of SV on option prices, as well as the interplay between SV and jumps, estimation of SV models with a focus on the simulation-based indirect inference as a generic approach and the efficient method-of-moments (EMM), and volatility forecasting based on standard volatility models and volatility forecasting using implied volatility from option prices. The relationship between option prices and underlying asset return dynamics offers guidance in searching alternative option pricing models that have the “right” distribution as implied from option prices. The SV model has a flexible distributional structure in which the correlation between volatility and asset returns serves to control the level of asymmetry and the volatility variation coefficient serves to control the level of kurtosis. It is obvious that implications of SV on option prices depend critically on the specification of the SV processes.