Option Pricing Under Stochastic Interest Ration And Monte Carlo Method

Options are derivative financial instruments based on futures on produce.Refers to a certain period in the future rights the underlying asset can be traded, which is the buyer pay a certain amount of money (referring to the premium) to the seller,then the buyer can have a right(but do not have the obligation) to buy or sell the underlying asset to the seller in advance provides a good price (the strike price means) at a period of time (refer to the American option) or a specific time (refer to the European option).Essentially speaking, Option is essentially rights pricing in the financial field in order to the assignee of the rights can decided whether to exercise of a power within the specified time,and obligations of parties have to be fulfilled.About the option pricing problem, Black-Scholes Option Pricing Model is the basis of option pricing, is widely used in options market,But the Black-Scholes formula also has a lot of limitations, it has to consider the interest rate is fixed value, and the actual situation in the volatility of interest rates is not consistent with the existence, So,compare to the actual price,Black-Scholes option pricing model will inevitably produce errors.To compensate for this error, stochastic interest rate models have emerged, which are more representative of the Vasicek model raised by Vasicek model and MHL model raised by Merton,Ho and Lee. Compared to the theory of pricing method, the Monte Carlo method and the binary method, finite difference methods belong to the numerical pricing method,Its essence is to predict the average return of the options and get an estimate of the option price by simulating the underlying asset price path,The biggest advantage of the Monte Carlo method is that the error rate of convergence O (n2) does not depend on the dimension of the problem, which is very suitable for high-dimensional option pricing.This article first has been studied basic Black-Scholes option pricing formula in detail, gives a detailed derivation of Black-Scholes option pricing model with the ba-sic result.Under the stochastic interest rate models, including Vasicek model and MHL under the model,gives the basic results of the European option,futhermore,Under the assumption of more general interest rate and the price of the asset, the drift coefficient and diffusion coefficient in order to adapt to the conditions of stochastic processes is presented the basic ideas of European option pricing,And got an underlying asset fol-lows geometric Brownian motion, interest rates, subject to the analytical solution of the HJM model of European option price.At last,option pricing method of monte carlo is studied, and the general conclusion is given and the results of numerical simulation.