Utility indifference option pricing model with a non-constant risk-aversion under transaction costs and its numerical approximation
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 trans...
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| Veröffentlicht in: | Journal of risk and financial management 2021-09, Vol.14 (9), p.1-12 |
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| container_title | Journal of risk and financial management |
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| creator | Pólvora, Pedro Ševčovič, Daniel |
| description | 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. |
| doi_str_mv | 10.3390/jrfm14090399 |
| format | Article |
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| identifier | ISSN: 1911-8074 |
| ispartof | Journal of risk and financial management, 2021-09, Vol.14 (9), p.1-12 |
| issn | 1911-8074 1911-8066 1911-8074 |
| language | eng |
| recordid | cdi_proquest_journals_2576449002 |
| source | MDPI - Multidisciplinary Digital Publishing Institute; EZB-FREE-00999 freely available EZB journals |
| subjects | Approximation Costs Expected utility finite difference approximation Hamilton-Jacobi-Bellman equation Hedging Markov analysis option pricing penalty methods Securities prices Stochastic models Stock prices transaction costs utility indifference pricing |
| title | Utility indifference option pricing model with a non-constant risk-aversion under transaction costs and its numerical approximation |
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