A time consistent derivative strategy

Walter Mudzimbabwe
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Walter Mudzimbabwe: Department of Mathematics, University of Zimbabwe, P. O. Box MP 167, Mount Pleasant, Harare, Zimbabwe2School of Computer Science and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein 2000, Johannesburg, South Africa

International Journal of Financial Engineering (IJFE), 2020, vol. 07, issue 01, 1-25

Abstract: In this paper, we derive a time consistent investment strategy for an investor who can invest not only in a bond and stock but in a derivative as well. In order to capture typical features shown by stocks, the stock and by extension the derivative depends on stochastic volatility. We assume that the investor is interested in maximizing a mean–variance utility function. Since the problem is time-inconsistent, we formulate the problem in game theoretic way and seek a subgame Nash equilibrium as the strategy. By solving an extended HJB equation system, we derive explicit time-consistent strategy and the corresponding efficient frontier. In order to show efficiency of the derivative strategy, we compare it with a strategy for the case of a market without a derivative. Our results show that efficient frontier for an investor with a derivative is higher than without derivative.

Keywords: Time consistent; equilibrium strategy; mean–variance optimization; stochastic volatility; derivative strategy (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S2424786320500048

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