In this paper we consider option pricing using multivariate models for asset returns. Specifically, we demonstrate the existence of an equivalent martingale measure, we characterize the risk neutral dynamics, and we provide a feasible way for pricing options in this framework. Our application confirms the importance of allowing for dynamic correlation, and it shows that accommodating correlation risk and modeling non-Gaussian features with multivariate mixtures of normals substantially changes the estimated option prices.

This paper introduces a class of Affine multivariate GARCH models. Our setting offers flexibility to accommodate stylized facts of asset returns like dynamic conditional correlation and a covariance dependent pricing kernel. The model admits a closed-form recursive representation for the moment generating function under both historical and risk-neutral measures, permitting efficient multi-asset option pricing and risk management calculations. We illustrate the applicability and impact of our framework on the five assets for which volatility indices are made publicly available, together with the S&P 500 Index. We demonstrate that our methodology is remarkably faster than Monte Carlo simulation when pricing two-assets options. We confirm the importance of incorporating a covariance-dependent pricing kernel compared to a linear pricing kernel by reporting large and economically significant changes in the price of two-asset options. Similarly, our single-factor Index model structure for the marginal can lead to differences of up to 70% in the price of single-asset options and empirical option pricing errors that are up to 41% smaller than what is obtained with a univariate model with a linear pricing kernel.

When it comes to individual stock option pricing, most applications consider a univariate framework. From a theoretical point of view this is unsatisfactory as we know that the expected return of any asset is closely related to the exposure to the market risk factors. To address this, we model the evolution of the individual stock returns together with the market index returns in a flexible bivariate model in line with theory. The model parameters are estimated using both historical returns and aggregated option data from the index and the individual stocks. We assess the model performance by pricing a large set of individual stock options on 26 major US stocks over a long time period including the global financial crisis. Our results show that the losses from using a univariate formulation amounts to 11% on average when compared to our preferred bivariate specification.