Quasi-Monte Carlo Algorithm for Pricing Options

Abstract

The purpose of this paper is to compare the use of Quasi-Monte Carlo methods, especially the use of recent developed (t, m, s)-nets, versus classical Monte Carlo method for valuing financial derivatives. Some research has indicate that under certain condition Quasi-Monte Carlo is superior than the traditional Monte Carlo in terms of rate of convergence and accuracy. In particular, theoretic results hinted that the so-called (t, m, s)-net suppose to be the most powerful one among all the Quasi-Monte Carlo methods when the problem is "smooth". However, the application of (t, m, s)-net was not included in the existing simulation literatures. In this paper I will introduce the algorithms of generate the most common Quasi-Monte Carlo sequences, then implement these sequences in several path-dependent options. Our investigation showed that Quasi-Monte Carlo methods outperform the traditional Monte Carlo.