二叉树期权定价中的到期时间择时研究  

Study on Timing of Expiration Time in Binomial Tree Option Pricing

作　　者：李冠宇 Guanyu Li(School of Economics and Management, Tongji University, 201804, Shanghai)

机构地区：[1]同济大学经管学院,上海市201804

出　　处：《数学计算（中英文版）》2019年第1期1-6,共6页Mathematical Computation

摘　　要：本文以标的物为股票的看涨期权为例,在二叉树模型的基础上,将股票价格的波动过程转化为直线上的随机游动。进而吸收H.Kesten,M.V.Kozlov和F.Spitzer1979年的研究成果,表明随机游动的首达时间可由一个分枝过程的人口数来刻画。以此为基础,本文计算出股票第一次(或第n次)上涨时间的概率生成函数,并对此生成函数进行泰勒展开,得到首达时所用不同时间的不同概率,分析股票波动的相关概率特征,并以此指导选择期权到期时间的研究。In this paper, we take the call option with stock as stock as an example. On the basis of the binary tree model, we convert the fluctuation process of stock price into random walk on the straight line. Furthermore, the results of H. Kesten, M.V. Kozlov and F. Spitzer in 1979 were used to show that the first arrival time of random walks can be characterized by the population of a branching process. Based on this, this paper calculates the probability generation function of the first (or nth) rise time of the stock, and performs Taylor expansion on the generated function to obtain different probabilities of different times used in the first arrival, and then analyzes its probability characteristics..Based on this, the study guides the selection of the option expiration time.

关 键 词：二叉树模型 首达时间 分枝过程 

分 类 号：O211.62[理学—概率论与数理统计]