Derivative Pricing under Multivariate Stochastic Volatility Models with Application to Equity Options

We examine the joint time series of option prices and returns on the S&P 500 index and a set of stocks drawn from the index with a new arbitrage-free multivariate stochastic volatility model that captures a market effect. The preliminary results show that the new model fits well for all the marginal time series for different periods of time. The price of volatility risk is estimated from option prices simultaneously for stocks and the index. We find that the volatility risk premia is not constant over time and that it differs across stocks. However, our model yields very small option pricing errors both in-sample and out-of-sample. Our future work will focus on (1) improving the estimation from the joint data of returns and option prices, and test the statistical significance of model parameters, (2) compare our modeling approach with existing univariate models from a trading perspective, and (3) extend our model with a latent process to describe the price of volatility risk.