美式期权的二叉树与三叉树定价模型收敛速度比较  

A Comparison of the Rate of Convergence between Binomial Model and Trinomial Model for Pricing American Options

作　　者：何颖俞[1] 

机构地区：[1]杭州师范大学数学系,浙江杭州310036

出　　处：《杭州师范学院学报（自然科学版）》2007年第6期424-429,共6页Journal of Hangzhou Teachers College(Natural Science)

基　　金：浙江省自然科学基金项目(Y604137)

摘　　要：美式期权不同于欧式期权,可以在到期日以前任意时间操作.一般而言,美式期权定价的解析解是很难得到的,二叉树和三叉树方法都是比较好的数值计算方法,它们都收敛于Black-Scholes期权定价公式的价格.在此对二叉树和三叉树模型的节点数目、近似误差和计算时间进行了比较,并且通过Visual Basic程序,给出实例说明三叉树模型要比二叉树模型在精确性方面要好,但是计算时间却要慢得多.An American option differs from a European one by the early exercise possibility.An American option can be exercised at any time up to the maturity date.In general,there is unfortunately no analytical solution to the American option problem.Binomial and trinomial approximations are useful to solve this problem.Both models have the property of convergence to Black-Scholes true price.This paper compares the rate of convergence.The comparison is based on the number of nodes produced,computer time used and the approximation error.An illustrative example is used to compare the convergence speed of these two models.These values are calculated by a Visual Basic code.

关 键 词：美式期权 BLACK-SCHOLES期权定价模型 二叉树模型 三叉树模型 

分 类 号：F830.9[经济管理—金融学]