Copyright © 2010 Tak Kuen Siu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.