Short rate analysis and marked point processes

In this paper we model the instantaneous spot interest rate in a financial market by means of a marked point process with bounded, predictable intensity. The transformed intensity of the point process vanishes when the interest rate leaves a prescribed bounded interval. We show that the pure discount bond price satisfies a partial differential difference equation under the risk-adjusted measure P <Superscript>*</Superscript>. Finally, we perform some numerical simulations of the discount bond price. Copyright Springer-Verlag Berlin Heidelberg 1999