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Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

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  • Pedro Pólvora

    (Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava, Slovakia)

  • Daniel Ševčovič

    (Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava, Slovakia)

Abstract

Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions solving the system of HJB equations. We introduce the transformation method for solving the penalized nonlinear partial differential equation. The transformed equation involves possibly non-constant the risk aversion function containing the negative ratio between the second and first derivatives of the utility function. Using comparison principles we derive useful bounds on the option price. We also propose a finite difference numerical discretization scheme with some computational examples.

Suggested Citation

  • Pedro Pólvora & Daniel Ševčovič, 2021. "Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation," JRFM, MDPI, vol. 14(9), pages 1-12, August.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:9:p:399-:d:621249
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    References listed on IDEAS

    as
    1. Jan Kallsen & Johannes Muhle-Karbe, 2015. "Option Pricing And Hedging With Small Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 25(4), pages 702-723, October.
    2. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
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