基于二叉树与三叉树期权定价的交替树图方法  

An Alternate Tree Method Based on Binomial and Trinomial Tree for Option Pricing

作　　者：宫文秀 许作良 GONG Wenxiu;XU Zuoliang(College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590;School of Mathematics,Renmin University of China,Beijing 100872)

机构地区：[1]山东科技大学数学与系统科学学院,青岛266590 [2]中国人民大学数学学院,北京100872

出　　处：《系统科学与数学》2021年第12期3478-3499,共22页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12071479,11571365)资助课题。

摘　　要：文章提出一种简单直观的交替树图离散时间模型用于期权定价.文章基于传统的二叉树和三叉树定价模型中存在的问题与特点,将二叉树与三叉树模型结合,构建了二叉树与三叉树交替的树图期权定价模型,讨论了模型的收敛性.利用该模型对欧式期权和美式期权定价分别进行了数值计算,并通过上证50ETF数据进行实证分析.数值结果表明,所提的交替树图定价方法对欧式期权、美式期权定价以及市场数据均是有效的,并且收敛速度与计算效率均比二叉树和三叉树方法有所提高.This article aims to propose a simple alternate tree discrete-time model for valuing options.Based on the problems and characteristics of traditional binomial tree and trinomial tree pricing models,this article combines the traditional binomial tree and the trinomial tree to construct a new alternate option pricing model,and discusses the convergence of the model.By using this model,the prices of European option and American option are numerically calculated respectively,and the empirical analysis is carried out through SSE 50 ETF data.The numerical results show that the proposed tree pricing method is effective for European options,American options pricing and market data,and the convergence speed and computation accuracy are improved compared with the binomial tree and the trinomial tree method.

关 键 词：二叉树 三叉树 交替树图 收敛性 期权定价 

分 类 号：O241[理学—计算数学] F832.5[理学—数学]