Study on Timing of Expiration Time in Binomial Tree Option Pricing

摘要

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.