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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 Polvora
  • Daniel Sevcovic

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.

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  • Pedro Polvora & Daniel Sevcovic, 2021. "Utility indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation," Papers 2108.12598, arXiv.org.
    • Handle: RePEc:arx:papers:2108.12598
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    References listed on IDEAS

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    1. Perrakis, Stylianos & Lefoll, Jean, 2000. "Option pricing and replication with transaction costs and dividends," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1527-1561, October.
    2. 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.
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    6. Anna Clevenhaus & Matthias Ehrhardt & Michael Günther & Daniel Ševčovič, 2020. "Pricing American Options with a Non-Constant Penalty Parameter," JRFM, MDPI, vol. 13(6), pages 1-7, June.
    7. Lesmana, Donny Citra & Wang, Song, 2015. "Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 318-330.
    8. W. Li & S. Wang, 2009. "Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 279-293, November.
    9. Sona Kilianova & Daniel Sevcovic, 2018. "Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio Optimization," Papers 1810.11619, arXiv.org.
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