Lower Bounds for Asian Options

There are two types of Asian options, fixed-strike and floating-strike, in the literature. We give lower bounds on the values of both fixed-strike and floating-strike Asian options in continuous case. Good lower bounds for both options have been derived earlier by Rogers & Shi (1995) and Thompson (1998). But the lower bound derived by them assumes a maturity of one year. This thesis extends Thompson’s version of the lower bound to the case of general maturities. Numerical experiments are performed to confirm the extreme accuracy of the lower bound.Table of Contents 1 Introduction 1 1.1 Background 1 1.2 Structures of the Thesis 3 2 Mathematical Preliminaries 4 2.1 Correlation Matrices 4 2.2 Basic Statistical Properties 6 3 Lower Bounds 8 3.1 Fixed-Strike Asian Options 8 3.2 Floating-Strike Asian Options 9 4 Numerical Results 12 5 Conclusions and Future Work 20 Appendix Proof for Theorem 2.5 21 Proof for Theorem 2.6 21 Bibliography 2