# How to estimate today's closing price?

I'm working on interday trading algorithm and I have a basic question:

How can I estimate today's closing price? I need it to predict tomorrow closing price. Should I use the price few moments before market close? However this could be too late to place orders and use my prediction of tomorrow price. Is my logic incorrect somehow? What is the common practice?

A famous model, made ubiquitous by Black, Scholes and Merton, is a geometric Brownian motion. Under this model, the stock price $S_T$ at time $T$ given the price $S_0$ at time $0$ is $$S_T = S_0e^{\left(\mu - \frac{\sigma^2}{2}\right)T + \sigma \sqrt{T}Z},$$ where $Z$ is a standard normal random variable. The expected value of the stock price under this model is $$E(S_T) = S_0e^{\mu T}.$$ You may use standard parameter estimation techniques to estimate the parameter $\mu$, such as maximum likelihood estimation (MLE). But, I should warn you that estimating the drift rate $\mu$ is notoriously inaccurate. Perhaps a user with more time series experience could suggest more robust models based on time series models, if that interests you.
• I think you forgot the $-\frac{\sigma^2}{2}$ term in the exponent in the expected value. – carbolymer Dec 26 '15 at 21:54