An information theoretic market index

Abstract

Nowadays, common indices act mainly as indicators of stock market performance and development. Since almost all of these indices are somehow a weighted average, thus, they are not able to answer the main question of investors, which is the likelihood that the status of a market changes or remains the same in next sessions. Therefore, by applying the principles of information theory we will try to suggest a new defined index as a new approach to stock market indicators. In this thesis, we suggest two different ways of market analysis; first, we consider a single stock option and second, we consider a family of stock options. In the first case, we mainly consider three type of information measures; entropy, entropy rate and relative entropy. In the second case, we consider two information measures; entropy rate and joint entropy. We also suggest several stochastic models as an estimate for stock price such as the Geometric Brownian motion model, with constant drift and volatility or with drift as a function of time, and Markov chain models. In addition, the analysis is carried by using models for the option price and the "rate of change" of the option price.