Pricing Asian Options and Basket Options by Monte Carlo Methods

Abstract

In this thesis, we investigate pricing Asian options and basket options under different Monte Carlo methods. It is observed that the prices of Asian options and basket options are based on the combinations of stocks prices, while the stocks follow a geometric Brownian motion (GBM). For the price of Asian options, a benchmark price is computed first. A partial differential equations (PDE) (one dimension in time and one in space) due to Veˇceˇr with the constant volatility of Asian call option is numerically solved and gives the option prices which we use as a benchmark. After that, three Monte Carlo methods are used to simulate Asian option prices: naive Monte Carlo, antithetic Monte Carlo and control variate. Comparing them with the benchmark and by evaluating the absolute error, mean square error and computation time, we eventually find that control variate method is the most efficient method for pricing Asian options. Next, to price basket options, we choose two different control variate, a classical one and a novel one. After applying these two control variates, we evaluate the performance by mean square error, length of 95% confidence interval and computation time. Taking all factors into consideration, the new control variate is more useful for pricing basket options.