呂育道臺灣大學：財務金融學研究所余軒Yu, HsuanHsuanYu2007-11-282018-07-092007-11-282018-07-092006http://ntur.lib.ntu.edu.tw//handle/246246/60699Basket option is an option whose payoff depends on the value of a portfolio of underlying assets. Basket option is challenging to price using conventional methods since the weighted sum of lognormal random variables is no longer lognormally distributed. American versions of basket options, i.e., where the owner have the right to exercise early, are particularly challenging to price. We introduce the idea of lognormal approximation and applying Ju’s (1998) method, we extend the idea to price American basket options. We found that the more positively correlated the underlying assets are, the more accurate this method would be. The main contribution of this thesis is that we propose a method to price American basket options efficiently, especially for short maturity options. We test this method for short maturity (4 months and 1 year) and long maturity (3 years) options. Numerical results illustrate the performance of the method.Contents 1 Introduction 1.1 Introduction ………………………………………………… 1 1.2 Organization of This Thesis ………………………………… 2 2 Fundamental Concepts in Option Pricing, Model Description, and Literature Review 2.1 Risk Neutral Pricing ………………………………………… 3 2.2 Model Description …………………………………………… 4 2.3 Literature Review …………………………………………… 7 3 Pricing European-Style Basket Options 3.1 The Lognormal Approximation ……………………………… 12 3.2 Taylor Series Expansion: Ju’s Method ……………………… 16 4 Pricing American-Style Basket Options 4.1 Optimal Stopping Problem ………………………………… 24 4.2 Lognormal Approximation …………………………………32 5 Numerical Results ……………………………………… 33 Appendix ………………………………………………………… 44 Bibliography ……………………………………………………… 49602237 bytesapplication/pdfen-US多資產選擇權評價一籃子選擇權美式選擇權蒙地卡羅法Multi-Asset Option PricingBasket OptionsAmerican OptionsMonte Carlo Methodthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/60699/1/ntu-95-R93723048-1.pdf