Inference and Computation for Stochastic Volatility Models related to Option Pricing

This paper reviews the Black-Scholes theory and studies a number of extensions. In particular, we focus on logarithmic stochastic volatility (SV) models and square-root SV models with jumps. Inference on those models, using Markov chain Monte Carlo methods, is summarized. Generalized Black-Scholes (GBS) pricing formulas are presented as an important step in calibration of SV models using both return and option data. A Gaussian approximation scheme is proposed to significantly reduce the dimensionality of certain stochastic integrals involved in the GBS formulas, which shows a great promise in improving computational efficiency.