The Pricing Of European Call Option In Black-Scholes Model With Coefficients Of Trapezoidal Fuzzy Number

The application of uncertain information processing and knowledge mining is an important part of human life,which involves many problems in real world.With the continuous development of human economy and society,the non-singularity,complexity and fuzziness of things also increases,making uncertain information applied to many financial fields.How to solve the problems of uncertain information in the field of relevant financial systems becomes an important issue.In the uncertainty analysis of finance,the people often use a series of fuzzy numbers to deal with the uncertain information in an intergraded way.It is not only helpful to inherit the original intention of classical prediction in the financial field,but also makes the results more in line with the objective law of finance.So far,there are many results about the application of fuzzy numbers in finance.Based on the previous studies,the financial model based on the theory of fuzzy numbers is studied.Therefore,using the concept of fuzzy numbers and correlative knowledge,the fuzzy numbers are applied to the coefficients of the financial model,and the specific expression of cut-set form of European call option pricing in the Black-Scholes model(the B-S model)with general fuzzy coefficients is given.In addition,in order to facilitate the practical application,on the one hand,the polygonal approximate expression of membership function of European call option pricing in the B-S model is created,but on the other hand,we can use the normal point set based on the trapezoidal fuzzy number and the end point of support set and the formal expression based on the trapezoidal fuzzy number cut set,respectively,to obtain the cut set expression and its membership function expression of European call option pricing in the B-S model,and eventually we can achieve the applications of the fuzzy number in the B-S model of financial model.The main work of this thesis lie in the following:1.In the chapter 1,a brief introduction of the development the background of fuzzy sets,fuzzy numbers and the research status of the B-S model are introduced.2.In the chapter 2,we introduced the mainly introduces concepts and properties of fuzzy sets,the membership functions and fuzzy numbers.It also introduces the concepts of European call option pricing in the B-S model of trapezoidal fuzzy number,preparefor the discussion that follows.3.In the chapter 3,we can use the concept of fuzzy numbers and the formal operation properties of cut sets.At first,on the basis of the analysis of the B-S model with general fuzzy coefficients,the specific expression of the cut-set form of European call option pricing in the B-S model with general fuzzy coefficients is given.Then,the polygonal approximate expression of the membership function of European call option pricing in the B-S model is given.Finally,the example is given to illuminate the validity of the cutset formal expression of European call option pricing in the B-S model and the polygonal approximate expression of the membership function of European call option pricing in the B-S model.4.In the chapter 4,For the convenience of application,we also use different processing methods to introduce trapezoidal fuzzy number into the B-S model.Firstly,we get the expression of cut set and the membership function of European call option pricing in the B-S model based on the expression of the normal point set of trapezoidal fuzzy number and the support set of endpoint.Secondly,we get the European call option pricing in the B-S model based on the operation property of trapezoidal fuzzy number cut set.The expression of valence cut set and membership function are given.Finally,we respectively through two examples illustrate the feasibility of its results.5.In the chapter 5,we summarize the article and prospect the problems to be studied in the article.