The risk-neutral stochastic volatility in interest rate models with jump–diffusion processes

Abstract

In this paper, we consider a two-factor interest rate model with stochastic volatility and we propose that the interest rate follows a jump–diffusion process. The estimation of the market price of risk is an open question in two-factor jump–diffusion term structure models when a closed-form solution is not known. We prove some results that relate the slope of the yield curves, interest rates and volatility with the functions of the processes under the risk-neutral measure. These relations allow us to estimate all the functions with the bond prices observed in the markets. Moreover, the market prices of risk, which are unobservable, can be easily obtained. Then, we can solve the pricing problem. An application to US Treasury Bill data is illustrated and a comparison with a one-factor model is shown. Finally, the effect of the change of measure on the jump intensity and jump distribution is analysed.