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.
Original language | English |
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Article number | 870516 |
Pages (from-to) | 1-18 |
Number of pages | 18 |
Journal | International Journal of Stochastic Analysis |
Volume | 2010 |
DOIs | |
Publication status | Published - 2010 |