Apply MC and QMC to price Asian options
Monte Carlo simulation (MC) is an approach that is widely used in high-dimensional numerical integration and one of its main financial applications is option pricing. The aim of this thesis is to evaluate the price of an Asian option using standard Monte Carlo method and Quasi-Monte Carlo method (QMC) respectively. Since QMC's convergence rate is determined by nominal problem dimension, the convergence rate of QMC increases as the problem dimension increases, which limits the performance of QMC in high dimensions. Hence, in this thesis, we also consider several techniques which are proposed to capture the effective dimensions and improve the efficiency of QMC in high-dimensional situations. The techniques include principal component analysis (PCA) and Kronecker product approximation (KPA) and they are applied for both constant and time-dependent volatilities. Finally, we conduct numerical experiments and compare the precision and computational time between Quasi-Monte Carlo and Monte Carlo methods.
PS. The instruction of running the codes could be found in codes.pdf