Contents
1 Introduction
1.1 Introduction 1
1.2 Organization of This Thesis 2
2 Background
2.1 Monte Carlo Simulation 3
2.2 Estimating the Greeks Using Simulation 4
2.3 Antithetic Variates 5
3 Quasi-Monte Carlo Methods
3.1 Low Discrepancy Sequences 6
3.1.1 Halton Sequences 7
3.1.2 Faure Sequences 8
3.1.3 Sobol Sequences 9
3.2 Pseudo Random Uniform Sequences 10
3.2.1 rand() 10
3.2.2 The Mersenne Twister 10
3.3 Normal Inversion Methods 11
4 Numerical Results
4.1 Evaluating Vanilla Call Options 13
4.2 Evaluating Rainbow Options 15
4.3 Evaluating Asian Options 18
5 Conclusions 20
Bibliography 21
Appendix 22