Estimation of the Pricing of Bond Options on the Arbitrage-Free Model with Jump Using Stochastic Simulation Procedure

This paper includes three contents for the pricing of bond options on the arbitrage-free model with jump. The first uses a new technique to derive a Closed-Form Solution (CFS) for bond options on Hull and White (HW) model with jump. The second, deals with the pricing of bond option for Heath-Jarrow-Morton (HJM) model based on jump, and the third simulates the proposed models by the Monte Carlo Simulation (MCS). We also analyze the values obtained by the CFS and MCS. There is substantial difference between bond options price which are obtained by the HW model with jump and the HJM model based on jump. For this, we use the well-known Mean Standard Error (MSE). We make sure that lower value of Precision (PCS) in the proposed models corresponds to sharper estimates. In particular, we confirm that the PCS for the HJM based on jump is lower than the HW model with jump. Though the empirical computer simulation, it means an accurate estimation for the pricing of bond options.