Department of Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia
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.
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.