JSM 2004 - Toronto

Abstract #300964

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Activity Number: 86
Type: Contributed
Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #300964
Title: Markov Models for Financial Time Series
Author(s): Stanley L. Sclove*+
Companies: University of Illinois, Chicago
Address: Information & Decision Sciences Dept. (MC 294), Chicago, IL, 60607-7124,
Keywords: stock prices ; EM algorithm ; rates of return ; hidden Markov model
Abstract:

In the classical geometric Brownian motion model for stock prices the difference of the logarithm of the price series (the continuous rate of return, ROR) is a sequence of independent identically distributed normal random variables. Problems in applying this model are (1) successive values of ROR may not be independent, and (2) the ROR may not be normally distributed. The Markov model (MM) used here postulates states and transitions between them. This MM can model dependence, and the states can have different distributions, e.g., different normal distributions. Both visible-state and hidden-state MMs are treated. In the hidden-state model the EM algorithm estimates both the states and the distributional parameters. A run of one state can be considered a segment. Segmenting macroeconomic series by MMs can provide objective definitions of phases of the economy: recession, recovery, and expansion. Segmenting stock indices can provide objective definitions of bull and bear markets. Fitting MMs to stock prices can provide alternative scenarios for portfolio optimization, trading strategy, and options pricing.

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Revised March 2004