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

[摘要] We investigate a Markov, regime-switching, marked point process for the short-terminterest rate in a market. The intensity of the marked point process is abounded, predictable process and is modulated by two observable factors. One isan economic factor described by a diffusion process, and another one is describedby a Markov chain. The states of the chain are interpreted as different ratingcategories of corporate credit ratings issued by rating agencies. We consider ageneral pricing kernel which can explicitly price economic, market, and creditrisks. It is shown that the price of a pure discount bond satisfies a system ofcoupled partial differential-integral equations under a risk-adjusted measure.

[学科分类] 应用数学