Estimating the half-life of stock price mean reverting: an application of Stochastic Differential Equations
Subject Areas : Statisticshadi rahmani fazli 1 , ahmad molabahrami 2
1 - عضو هیئت علمی و استادیار گروه اقتصاد سیاسی و سیاست گذاری عمومی ، دانشکده حقوق و علوم سیاسی، دانشگاه علامه طباطبایی، تهران، ایران.
2 - shahid beheshti university
Keywords: mean reversion, half-life, Unit root test, stochastic differential equations.,
Abstract :
In this paper we use stochastic differential equation for estimating the long run equilibrium of the stock prices, the speed of reverting to the mean of the stock prices and the half-life of the stock prices of the selected firms (about 24 active firms) in Tehran Stock Exchange. We use the stock price data of the selected firms to see if the stock prices of these firms have Unit roots tests. For firms which their stock prices are stationary, without unit roots, we follow an Ornstein-Uhlenbeck stochastic differential equation to estimate the half-life of the stock returns of the selected firm. For firms which their stock prices have got the unit root, we use Geometric Brownian Motion for estimation. The results show that most of the studied companies have a reversible behavior to a long-term average and a half-life of stock prices is estimated to be from 3 to 30 weeks. The estimation of the half-life of the stock prices of the selected firms will provide valuable information for the investors and other agents active in the stock markets.