Binary Tree Model With Fuzzy Coefficients And European Call Option Pricing

With the development of modern science and technology,the application of fuzzy mathematics is more and more extensive,and its role in the financial field is also increasingly prominent.Owing to the fluctuation of financial market from time to time,the risk-free interest rate,volatility and stock price may have uncertainty attributes in the real world.In other words,in financial activities,there are many cases involving not only some events that cannot be determined whether they occurs or not,but also some quantities without clear conceptual boundaries.For example,in the binary tree model,the price of the stock at the next time is usually just a predicted quantity,it is just an estimate of one quantity in the future.When we discuss some financial problems under fuzzy environment,it is more reasonable to use a fuzzy number or interval number than a crisp real number to express such an uncertain or imprecise quantity.Based on the binomial tree model with trapezoidal fuzzy number coefficient,this thesis studies the option pricing and membership function expression of trapezoidal fuzzy number binomial tree model by using the normal point set and support set endpoint of trapezoidal fuzzy number.Then,in order to discuss more general,we discuss the binomial tree model with general fuzzy number as coefficient,and deduce its fuzzy set(or number)option pricing expression.For the convenience of application,this thesis introduces the option pricing of the fold line fuzzy set(or number),and gives the specific steps and methods of the option pricing of the fold line fuzzy set(or number).The main contents of this thesis are as follows:In Chapter 1,the background and development of fuzzy number and fuzzy set are summarized,and the research status of fuzzy binary tree model option pricing are introduced.In Chapter 2,the concepts of fuzzy sets and fuzzy numbers are introduced,as well as the pricing of European call options based on the classical binary tree model,which paves the way for the next research in this thesis.In Chapter 3,the option pricing are studied based on trapezoid fuzzy number binary tree model.By converting the fuzzy number coefficients binary tree model into four classical binary tree models,a trapezoidal fuzzy number option pricing is defined,and two calculation formulas to solve the trapezoidal fuzzy number option pricing are obtained.One calculation formula is that the more general conditions hold and the other calculation formula is established under some special conditions.At last,we give an example to illustrate the feasibility of our method.In Chapter 4,the option pricing are studied based on fuzzy number binary tree model.By using the operation rules of fuzzy number addition and number multiplication in cut set form,the fuzzy number binary tree model is equivalently transformed into two families of classical binary tree models which change with the level value,the method of constructing fuzzy set(or number)option price by using two option price functions derived from the two families of classical binomial tree models is given.And then,for the convenience of practical application,the concepts of fold line fuzzy set option price and fold line fuzzy number option price are introduced,a sufficient condition for fold line fuzzy set option price to be fold line fuzzy number option price and a solution theorem of the fold line fuzzy number option price are obtained,and a specific solution method of the fold line fuzzy set option price and the fold line fuzzy number option price are set up.At last,two specific examples are given to show how to solve the fold line fuzzy set option price and the fold line fuzzy number option price.In Charter 5,the work of this thesis is summarized and the future research is prospected.