The Reduction of Forward Rate Dependent Volatility HJM Models to Markovian Form: Pricing European Bond Option

Ram Bhar, Carl Chiarella (), Nadima El-Hassan () and Xiaosu Zheng
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Ram Bhar: School of Banking and Finance, University of New South Wales

No 36, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: We consider a single factor Heath-Jarrow-Morton model with a forward rate volatility function depending upon a function of time to maturity, the instantaneous spot rate of interest and a forward rate to a fixed maturity. With this specification the stochastic dynamics determining the prices of interest rate derivatives may be reduced to Markovian form. Furthermore, the evolution of the forward rate curve is completely determined by the two rates specified in the volatility function and it is thus possible to obtain a closed form expression for bond prices. The prices of bond options are determined by a partial differential equation involving two spatial variables. We discuss the evaluation of European bond options in this framework by use of the ADI method.

Date: 2000-03-01
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