Option Pricing and a Comparison on the Dimension Reduction Techniques using Markov Chain Quasi-Monte Carlo under Random Sobol Sequences

Reduction technique improves the efficiency of quasi-Monte Carlo methods (QMC), and since different techniques have different efficiencies, in this paper, three methods are studied: Standard method (SM), Brownian Bridge (BB), and principal component analysis (PCA). Effective dimension theory and the efficiency of quasi-Monte Carlo method are also explained. The dimension reduction techniques typically concentrate on variance on the initial variables and on the first-order of prices, therefore, they can reduce the effective dimensions and as a result improve the efficiency of QMC.