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2006•Statistics & Risk ModelingRequires access

On Markovian short rates in term structure models driven by jump-diffusion processes

Pavel V. Gapeev, Uwe Küchler

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Abstract

In this paper a bond market model and the related term structure of interest rates are studied where prices of zero coupon bonds are driven by a jump-diffusion process. A criterion is derived on the deterministic forward rate volatilities underwhich the short rate process isMarkovian. In the case that the volatilities depend on the short rate sufficient conditions are presented for the existence of a finite-dimensional Markovian realization of the term structure model.

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What this paper is about

In this paper a bond market model and the related term structure of interest rates are studied where prices of zero coupon bonds are driven by a jump-diffusion process. A criterion is derived on the deterministic forward rate volatilities underwhich the short rate process isMarkovian. In the case that the volatilities depend on the short rate sufficient conditions are presented for the existence of a finite-dimensional Markovian realization of the term structure model.

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Available abstract

In this paper a bond market model and the related term structure of interest rates are studied where prices of zero coupon bonds are driven by a jump-diffusion process. A criterion is derived on the deterministic forward rate volatilities underwhich the short rate process isMarkovian. In the case that the volatilities depend on the short rate sufficient conditions are presented for the existence of a finite-dimensional Markovian realization of the term structure model.

Key concepts: Term (time), Jump diffusion, Zero-coupon bond, Forward rate, Short rate, Jump, Statistical physics, Markov process

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