Pricing and Risk Management with Stochastic Volatility Using Importance Sampling

Abstract

In this paper, we apply importance sampling to Heston's stochastic volatility model and the Bates's stochastic volatility with jumps. We propose an effective numerical scheme that dramatically improves the speed of importance sampling. Most importantly, we introduce the Likelihood Ratio Method Based on Characteristic Function to estimate the Greeks in a computationally efficient manner. To achieve significant variance reduction also for the Greeks, we combine this method with importance sampling. All results are illustrated using European and barrier options.