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Stochastic volatility for utility maximizers — A martingale approach

Author

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  • Simon Ellersgaard

    (Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark)

  • Martin Tegnér

    (Department of Engineering Science, Oxford-Man Institute of Quantitative Finance, University of Oxford, Parks Road, OX1 3PJ Oxford, England)

Abstract

Using Martingale methods, we study the problem of optimal consumption-investment strategies in a complete financial market characterized by stochastic volatility. With Heston’s model as the working example, we derive optimal strategies for a constant relative risk aversion (CRRA) investor with particular attention to the cases where (i) she solely seeks to optimize her utility for consumption, and (ii) she solely seeks to optimize her bequest from investing in the market. Furthermore, we test the practical utility of our work by conducting an empirical study based on real market-data from the S&P500 index. Here, we concentrate on wealth maximization and investigate the degree to which the inclusion of derivatives facilitates higher welfare gains. Our experiments show that this is indeed the case, although we do not observe realized wealth-equivalents as high as expected. Indeed, if we factor in the increased transaction costs associated with including options, the results are somewhat less convincing.

Suggested Citation

  • Simon Ellersgaard & Martin Tegnér, 2018. "Stochastic volatility for utility maximizers — A martingale approach," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-39, March.
    • Handle: RePEc:wsi:ijfexx:v:05:y:2018:i:01:n:s242478631850007x
    DOI: 10.1142/S242478631850007X
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    References listed on IDEAS

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