Affine multivariate GARCH models

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.