A Comparative Study Of Monte Carlo Simulation And Quasi - Monte Carlo Simulation In Option Pricing

Options, together with other financial derivatives, do play very important role in the financial market. With the development and innovative construction of Chinese financial market, options market will be available sooner or later, since we have successful futures market. Option pricing is of great significance because precise option pricing can smooth the market and give efficient information to investors.There are three methods aiming to solve the option pricing problem,the partial derivative equation method, the martingale method and the numerical method. Monte Carlo method is one of the numerical methods. Monte Carlo method is efficient in path-dependent situations, since it is a forward-solving kind. The weaknesses of Monte Carlo includes low convergence rate, low accuracy and time-consuming. Quasi-Monte Carlo (QMC) method, or low-discrepancy method is an improvement of traditional Monte Carlo method. The convergence rate of QMC isO(1/n), which is much higher than O(1/√n) of the traditional Monte Carlo, which will bring high accuracy and efficiency to the simulation.This paper is aimed at make a comparison between the MC and QMC method in option pricing. I study the properties of both methods in generating random numbers and random variables. I do the empirical study with one basic low-discrepancy sequence, Halton sequence to verify that QMC do better in generating random normal distributed variables. Thus, the result of simulation is better when using QMC. The option prices are more accurate with QMC method referring to BS results.The innovative things in this paper includes firstly, doing all the empirical study by using Matlab programming for simulation of both methods. Secondly, the study of Halton sequence in details. Thirdly, the comparison of the simulation results of both methods is convincing.