Short Rate Analysis and Marked Point Short Rate Analysis and Marked Point Processes

Allanus H. Tsoi

Department of Mathematics, Hong Kong University of Science and Technology (matsoi@ust.hk)

Abstract

In their work in 1994 Babbs and Webber dealt with an imcomplete market, in which they exhibited a martingale measure which is consistent with general equilibrium. They modelled the spot rate as a linear combination of Poisson processes. In this talk we use a marked point processs with bounded, predictable intensity to model the spot rate. We consider a state process which is a diffusion and is observable. We consider an equivalent martingale measure which is similar to that of Babbs and Webber. The transformed intensity of the point process vanishes when the spot rate leaves a prescribed bounded interval. We also consider the pure discount bond price which depends on the spot rate and the state process, and we show that the bond price satisfies a partial differential difference equation under the risk-adjusted measure. By using a varying grid method we are able to perform numerical simulation of the discount bond price where we interpret the state process as a magnification of the market rate.

This is joint work with Robert Elliott (University of Alberta) and Shiu-Hong Lui (Hong Kong University of Science and Technology).


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On 21 May 1999, 15:12.