American Option Pricing In The Model Of Discrete Time

Options are the most important derivatives in modern financial market,their pricing is also one of the most attractive topics in financial sector.The classical model of Black-Scholes has solved the European option pricing problems basically,but for American option,it has no fixed option exercise date and corresponding analytical formula,can not abtain exact solution,so American option pricing is a study hopspot.In terms of the continuity of time,the papers of studying the option pricing are divided into two categories:continuous-time option and discrete-time option.From a practical point of view,the study of discrete-time option is more closer to reality.This article will focus on discrete case of the American option pricing,firstly,describes option development and related concepts,classifications,summarizes the study of the status quo and gives the principal prior knowledge of mathematics the paper used;secondly,considering the American option utility maximization problem,bases on the standard American call option and standard American put option pricing model,uses martingale methods and optimal stopping theory,different utility functions are discussed under the American option utility maximization , for example , power utility function ,homogeneous utility function,American Boston utility function;and through a combination of different utility function reflects the different risk attitude studies the American option pricing based on different risk attitude.The numerical calculation method in American option pricing problem is very important.In the empirical analysis,how to obtain volatility is a key issue.This paper summarizes the study of the volatility, and divides it into three kinds:constant volatility,random volatility and fuzzy volatility,and discuss them respectively.In 2003,the Japanese scholar Yoshida introduced fuzzy theory to option pricing,and S.Muzzioli studied it further,fuzzy option pricing research is relatively few at present.We will be on the base of predecessors gives the fuzzy binomial tree model of American put option,and extend it to the gerenal utility function under the American option,and gives an example.