Estimation and Simulation of Bond Option Pricing on the Arbitrage Free Model with Jump

In pricing and hedging with financial derivatives, term structure models with jump are particularly important [1], since ignoring jumps in financial prices may cause inaccurate pricing and hedging rates [2]. Solutions of term structure model under jump-diffusion processes are justified because of movements in interest rates displaying both continuous and discontinuous behaviors [3]. Moreover, to explain term structure movements used in the latent factor models, it means how macro variables affect bond prices and the dynamics of the yield curves [4]. Current research using jump-diffusion processes relies mostly on two classes of models: the affine jump-diffusion class [5] and the quadratic Gaussian [6]. We consider the classes of HW model with jump and HJM model based on jump to investigate a CFS for bond option price on the proposed models. In this paper, we show the actual proof analysis of the HJM model based on jump easily under the extended restrictive condition of Ritchken and Sankarasubramanian (RS) [7]. By beginning with certain forward rate volatility processes, it is possible to obtain classes of interest models under HJM model based on jump that closely resembles the traditional models [8]. Finally, we confirm that there is a substantial difference between bond option prices which are obtained by HW model with jump and HJM model based on jump through the empirical computer simulation which used MCS, which is used by many financial engineers to place a value on financial derivatives. For this, we use the well-known MSE. We make sure that lower value of PCS in the proposed models corresponds to sharper estimates [9]. In particular, we confirm that the PCS for the HJM based on jump is lower than the HW model with jump. These results mean an accurate estimate in the empirical computer. The structure of the remainder of this paper is as follows. In section 4, investigate the pricing of bond on arbitrage-free models with jump. In section 4, the pricing of bond option on arbitrage-free models with jump are presented. Section 6, explains the simulation procedure of the proposed models using MCS. In Section 7, the proposed models’ performances are evaluated based on simulations. Finally, Section 8 concludes this paper. The Pricing of Bond on Arbitrate-Free Model with Jump