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A Markov Regime-Switching Marked Point Process for Short-Rate Analysis with Credit Risk

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  • Tak Kuen Siu

Abstract

We investigate a Markov, regime-switching, marked point process for the short-term interest rate in a market. The intensity of the marked point process is a bounded, predictable process and is modulated by two observable factors. One is an economic factor described by a diffusion process, and another one is described by a Markov chain. The states of the chain are interpreted as different rating categories of corporate credit ratings issued by rating agencies. We consider a general pricing kernel which can explicitly price economic, market, and credit risks. It is shown that the price of a pure discount bond satisfies a system of coupled partial differential-integral equations under a risk-adjusted measure.

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  • Tak Kuen Siu, 2010. "A Markov Regime-Switching Marked Point Process for Short-Rate Analysis with Credit Risk," International Journal of Stochastic Analysis, Hindawi, vol. 2010, pages 1-18, December.
    • Handle: RePEc:hin:jnijsa:870516
    DOI: 10.1155/2010/870516
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    Cited by:

    1. López, Oscar & Oleaga, Gerardo & Sánchez, Alejandra, 2021. "Markov-modulated jump-diffusion models for the short rate: Pricing of zero coupon bonds and convexity adjustment," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.

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