We determine the optimal portfolio for an ambiguity averse investor who has access to stock and derivatives markets. The stock price follows a stochastic volatility jump-diffusion process and the investor can have different levels of uncertainty about the diffusion parts of the stock and its volatility. We find strong evidence that the optimal exposures to stock and volatility risks are significantly affected by the ambiguity aversion to the corresponding risk factor only. We also show that volatility ambiguity has a smaller impact in incomplete markets. Investors who ignore jump risk/model uncertainty/derivatives always incur welfare losses. In our numerical example, the loss from neglecting model uncertainty can be almost as much as the loss from not trading the derivatives.

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.