Kisoeb Park

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

Three contents for the pricing of bond options on the arbitrage-free model with jump are included in this paper. 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 a substantial difference between bond option prices 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) and show 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 that for the HW model with jump. Through the empirical simulation of our method suggested, we obtain a better accurate estimation for the pricing of bond options.

On Sharp Estimating of Bond Option Prices for Heath-Jarrow-Morton Model Based on Jump

We propose Heath-Jarrow-Morton (HJM) model in which the forward rate follows a jump-diffusion process. We represent HJM model based on jump and give the analytic proof for it. We derive a closed-form solution of the European bond option for HJM model based on jump. We get the fact that bond option price for the proposed model estimate highly precision. Furthermore, we simulate the proposed model by Monte Carlo method with scenarios. Lower value of precision of bond option price for HJM model based on jump means sharper estimates.

Simulation Analysis for the Pricing of Bond Option on Arbitrage-Free Models with Jump

We derive a closed-form solutions for bond option pricing on arbitrage-free models with jump and perform Monte Carlo simulation for them. We know that the bond option price on arbitrage-free models with jump is humped. The fact shows that valuations of this model estimate highly precision. In this paper, we simulate the proposed models by the Monte Carlo simulation with scenarious. By simulation analysis, we obtain that bond option prices on arbitrage-free models are larger than bond option prices on arbitrage-free models with jump. Lower value of precision in arbitrage-free models with jump correspond to sharper estimates.

Statistical Prediction for the Pricing of Bond Using Random Number Generation

In this paper, we propose a dynamic prediction algorithm to predict the interest rate for the bond price using real data set. Our algorithm is based on term structure model of the interest rate, which takes place in financial modelling, such as the standard Wiener process. We use cumulative distribution function (CDF) of real data for the interest rate measurement. The CDF is obtained by the natural cubic spline (CS) method, which is the frequently used numerical methods for interpolation. Most useful when the CDF F(x) has an inverse Fi¾? 1(x) which is easy to compute. We use the random number generation to calculate the pricing of bond. In empirical computer simulation, we show that the lower values of precision in the proposed prediction algorithm corresponds to sharper estimates. It is very reasonable on prediction.

On multicast routing based on route optimization in network mobility

Mobile IP (MIP) is designed for supporting mobile nodes. However, the technology does not sufficiently handle NEtwork MObility (NEMO). The NEMO Basic Support (NBS) [1] ensures session continuity for all the nodes in a MObile NETwork (MONET). Since the protocol is based on MIP, when used to support multicast for NEMO, it inherits the same fundamental problems as MIP, such as tunnel convergence. Recently, many Route Optimization (RO) schemes have been proposed for the pinball routing problem in NEMO. And we should use the RO schemes for multicasting in NEMO. However, the tunnel convergence problem may be remained as unsolvable problem. Hence, we propose the similar source-based routing multicast scheme. In this paper, we present the multicast scheme based on well-known RO scheme Path Control Header (PCH) [2] in NEMO environments. Furthermore, the proposed schemes recovery time is more efficient than other well-known multicast schemes.

Stochastic simulation method for the term structure models with jump

Monte Carlo Method as a stochastic simulation method is used to evaluate many financial derivatives by financial engineers. Monte Carlo simulation is harder and more difficult to implement and analyse in many fields than other numerical methods. In this paper, we derive term structure models with jump and perform Monte Carlo simulations for them. We also make a comparison between the term structure models of interest rates with jump and HJM models based on jump. Bond pricing with Monte Carlo simulation is investigated for the term structure models with jump.

Bond pricing with jumps and monte carlo simulation

We derive a general form of the term structure of interest rates with jump. One-state models of Vasicek, CIR(Cox, Ingersol, and Ross), and the extended model of the Hull and White are introduced and the jump-diffusion models of the Ahn & Thompson and the Baz & Das as developed models are also investigated by using the Monte Carlo simulation which is one of the best methods in financial engineering to evaluate financial derivatives. We perform the Monte Carlo simulation with several scenarios even though it takes a long time to achieve highly precise estimates with the brute force method in terms of mean standard error which is one measure of the sharpness of the point estimates.

On monte carlo simulation for the HJM model based on jump

We derive a form of the HJM model based on jump. Heath, Jarrow, and Morton(HJM) model is widely accepted as the most general methodology for term structure of interest rate models. We represent the HJM model with jump and give the analytic proof for the HJM model with jump. We perform the Monte Carlo simulation with several scenarios to achieve highly precise estimates with the brute force method in terms of mean standard error which is one measure of the sharpness of the point estimates. We have shown that bond prices in HJM jump-diffusion version models of the extended Vasicek and CIR models obtained by Monte Carlo simulation correspond with the closed form values.