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

Abstract EN

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.