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

34 Pages Posted: 19 May 2015

See all articles by Simon Nielsen

Simon Nielsen

University of Copenhagen - Department of Mathematical Sciences

Martin Jönsson

University of Copenhagen - Institute for Mathematical Sciences

Date Written: May 15, 2015

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

Suggested Citation

Nielsen, Simon and Jönsson, Martin, Stochastic Volatility for Utility Maximisers - A Risk to Be Hedged? (May 15, 2015). Available at SSRN: https://ssrn.com/abstract=2606759 or http://dx.doi.org/10.2139/ssrn.2606759

Simon Nielsen (Contact Author)

University of Copenhagen - Department of Mathematical Sciences ( email )

Copenhagen
Denmark

Martin Jönsson

University of Copenhagen - Institute for Mathematical Sciences ( email )

Solbjerg Plads 3
Copenhagen, DK-2100
Denmark

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