基于三角直觉模糊数的欧式期权二叉树定价模型  

Binomial tree model of the European option pricing based on the triangular intuitionistic fuzzy numbers

作　　者：张茂军[1,2] 秦学志[3] 南江霞[2] 

机构地区：[1]上海交通大学上海高级金融学院,上海200030 [2]桂林电子科技大学数学与计算科学学院,桂林541004 [3]大连理工大学工商管理学院,大连116024

出　　处：《系统工程理论与实践》2013年第1期34-40,共7页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71001015;71171032;71172136;71101033);高等学校博士学科点专项科研基金(20090041110009);广西教育厅项目(201106LX162);广西自然科学基金(2012GXNSFAA053013)

摘　　要：为了刻画欧式期权价格估计值的不确定性和投资者的犹豫程度,用三角直觉模糊数表示期权标的资产价格的变化因子,构建了三角直觉模糊数二叉树定价模型,并用风险中性定价方法研究单期欧式看涨期权的定价问题.研究发现:欧式看涨期权价格表示为一个三角直觉模糊数,其值体现了投资者对期权价格估计值的肯定程度、否定程度和犹豫程度:利用三角直觉模糊数的截集运算法则得到了欧式看涨期权价格的区间值.数值算例表明,用三角直觉模糊数得到的欧式看涨期权的价格比用三角模糊数得到的价格更能体现投资者的犹豫性.In this paper the triangular intuitionistic fuzzy numbers are used to express the change factors of the underlying assets of the option in order to describe the uncertainty of the estimated value of the European option price and the hesitation degree of the investors, the intuitionistic fuzzy binomial tree pricing model is made, and the risk neutral pricing method is used to research the single period European call option pricing problem. The findings of the study are that the European option price expressed by a triangular intuitionistic fuzzy number, which can reflect the certainty degree, negation degree and hesitation degree of the investor on the estimated value of the option price, and then the interval value of European option price is obtained by using the cuts sets operation of the triangular intuitionistic fuzzy numbers. Some numerical examples show that European call option price obtained by the triangular intuitionistic fuzzy number can express more the hesitation degree of the investors than the one obtained by the fuzzy number.

关 键 词：欧式期权 三角直觉模糊数 二叉树模型 风险中性概率 

分 类 号：F830[经济管理—金融学]