Pricing Analysis On The Arithmetic Average Asian Option

In this paper, we take the arithmetic average asian call option pricing as anexample in order to compare advantages and disadvantages of Monte Carlo with ofQuasi-Monte Carlo in option pricing. Concrete step is to increase the number ofdimensions in order to compare the two methods’ difference in low-dimension andhigh-dimension. The result is that Quasi-Monte Carlo method is better than MonteCarlo Method both for low-dimension and for high-dimension after a short phasefluctuation, so we could know that Quasi-Monte Carlo method is better than MonteCarlo method in most of cases. On specific methods, we use Monte Carlo Method inuniform random number generation and Quasi-Monte Carlo Method in the lowdiscrepancy sequences of HALTON, FAURE and SOBOL etc, and generate theabove points through inverse transform into standard normal distribution points. Onthe path generating, sequentially, we use Random Walk, Brownian Bridge andPrincipal Component Analysis. On control variable choosing, we choose thegeometric average asian call option price’s analysis solution as the control variable toestimate the arithmetic average asian option price. To calculate the arithmetic averageasian call option price variance, due to the sequences by the proposed Quasi-MonteCarlo method are determinate low discrepancy sequences, variance therefore couldnot be calculated, so we introduce randomized Quasi-Monte Carlo Method.Specifically, when the dimension d is less than or equal to13, Quasi-Monte CarloMethod is better, then for further simulation with dimension being greater than13of30,50,100,361, the estimated effect of Quasi-Monte Carlo Method is better thanMonte Carlo Method with the increasing number of dimension in most of cases. Sowe think Quasi-Monte Carlo method is used to solve the high dimensional financialproblems more effectively, produce fewer errors, and cause more stable calculationsthan Monte Carlo Method. After the control variable method is used to Quasi-MonteCarlo and Monte Carlo, we discover variance is largely reduced, so control variablemethod is a very effective tool for controlling variance.