Optimal investment in equity and VIX derivatives

Abstract

We solve in closed-form the optimal investment strategies in equity and VIX derivatives in a stochastic volatility model with jumps. Our framework includes both complete market and incomplete market cases, when diffusive risk, volatility risk and jump risk are present. VIX derivatives allow for direct exposure to volatility risk compared to equity derivatives. Based on the closed-form formula, we explicitly determine the portfolio improvement brought by the inclusion of the VIX derivative and establish that it is theoretically positive. This justifies the economic intuition and observed demand for VIX derivatives in a portfolio management setting. Numerical examples illustrate the results.