On Interest Rate Option Pricing with Jump Processes

In this study, we investigate the pricing of interest rate options in three arbitrage-free models with jump process which are Vasicek and Cox-Ingersoll-Ross (CIR) models of stochastic interest rate and Heath-Jarrow-Morton (HJM) model for stochastic forward rate. Solutions of Hull and White (HW) type model with jump are derived directly using a system of differential equations and the relationship between short rate and forward rate processes which is obtained under the extended restrictive condition on jump and volatility can be used to have the formula of bond price. We also analyse the option values of three proposed jump models obtained by Monte Carlo simulations.