Application Of Monte Carlo In Two Types Of Path-dependent Option Pricing

With rapid development of global financial markets, derivatives was wel-comed by more and more investors. In today’s international financial mar-kets in addition to the transaction of European, American and other stan-dard options, it also emerged lots of other exotic options. Among them, path-dependent option is an important one. Its value depends on the price of under-lying assets during the term of the option. Path-dependent options are divided into strong path-dependent option and weak path-dependent option, of which the most important ones are Asian Option and Barrier Option. Monte Carlo method is a good way to price path-dependent option because it can simulate the complete path of the underlying assets price.But for Monte Carlo method, its variance is usually big. In order to reduce the variance, variance reduction techniques have been proposed, including Con-trol Variates, Antithetic Variates, Stratified Sampling, Important Sampling, Conditional Monte Carlo and so on. In addition, as an improved Monte Car-lo method, people use low-discrepancy sequences instead of pseudo-random number sequence, resulting in a new simulation method-Quasi Monte Carlo Method. An important advantage of Monte Carlo is the stability under high dimension, solving the "curse of dimensionality". As an improved method, Quasi-Monte Carlo is still applicable in pricing of high dimensional options.This paper mainly consists of two research work. The first is to price barrier option with Monte Carlo method, and use Important Sampling and Conditional Monte Carlo techniques to reduce variance. The second is the application of Quasi-Monte Carlo in high dimension. Based on the compare and analysis of Halton and Sobol’sequences, we apply these two low-discrepancy sequences to different dimensions of geometric average Asian option, to confirm the applicability in pricing of high dimensional option.