Stochastic Volatility for Utility Maximisers - A Risk to Be Hedged?

Abstract

From an empirical perspective, the stochasticity of volatility is manifest, yet there have been relatively few attempts to reconcile this fact with Merton's theory of optimal portfolio selection for wealth maximising agents. In this paper we present a systematic analysis of optimal asset allocation for the Heston model, the 3/2 model, and a Fong Vasicek type model. Under the assumption that the market price of risk is proportional to volatility, we can derive closed form expressions for the optimal portfolio using the formalism of Hamilton-Jacobi-Bellman. We also perform an empirical investigation, which strongly suggests that there in reality are no tangible welfare gains associated with hedging stochastic volatility.

Keywords: Merton's Portfolio Problem, Stochastic Volatility, HJB Equation

JEL Classification: C00, C50, C61