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On Valuation With Stochastic Proportional Hazard Models In Finance

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  • AKIRA YAMAZAKI

    (Graduate School of Business Administration, Hosei University, Japan)

Abstract

While the proportional hazard model is recognized to be statistically meaningful for analyzing and estimating financial event risks, the existing literature that analytically deals with the valuation problems is very limited. In this paper, adopting the proportional hazard model in continuous time setting, we provide an analytical treatment for the valuation problems. The derived formulas, which are based on the generalized Edgeworth expansion and give approximate solutions to the valuation problems, are widely useful for evaluating a variety of financial products such as corporate bonds, credit derivatives, mortgage-backed securities, saving accounts and time deposits. Furthermore, the formulas are applicable to the proportional hazard model having not only continuous processes (e.g., Gaussian, affine, and quadratic Gaussian processes) but also discontinuous processes (e.g., Lévy and time-changed Lévy processes) as stochastic covariates. Through numerical examples, it is demonstrated that very accurate values can be quickly obtained by the formulas such as a closed-form formula.

Suggested Citation

  • Akira Yamazaki, 2013. "On Valuation With Stochastic Proportional Hazard Models In Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 1-34.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:03:n:s0219024913500179
    DOI: 10.1142/S0219024913500179
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    References listed on IDEAS

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    1. Antje Berndt & Rohan Douglas & Darrell Duffie & Mark Ferguson, "undated". "Measuring Default Risk Premia from Default Swap Rates and EDFs," GSIA Working Papers 2006-E31, Carnegie Mellon University, Tepper School of Business.
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