算術平均一籃子選擇權之評價

Abstract

Basket 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.