Financial

Saint-Petersburg State University Faculty of Physics and DATAART company

Experimental Program of Supplementary Education "Information Technologies, Econophysics, and Complex Systems Management"

Internship Project

"Prediction of Financial Data Volatility Using the Multifractal MSM Model"

Accomplished by E.A Shalaginov
Supervised by L.A. Dmitrieva

This work is dedicated to prediction of financial time series volatility on the basis of the multifractal MSM model (Markov Switching Multifractal Model). For reader’s convenience the paper includes basic facts about fractals, multifractals, and their characteristics as well as the short description of the multifractal MSM model. Within the MSM model framework the explicit formulae for volatility prediction for various time horizons were elaborated. The model parameters were fitted for nine financial instruments of the US stock market (shares and stock indices) and the volatility forecasts for horizons from 1 to 50 days were created for these instruments.

The statistical comparison of the prediction accuracy was carried out for MSM and GARCH models. The latter model which is commonly used for volatility prediction was selected as a reference model. The comparison results showed that for the data used in the research in many cases the MSM model predicted volatility more accurately than GARCH. The paper also proposes several ways for the MSM model generalization in order to achieve better statistical quality of forecasts.

The volatility forecasts created with the use of the MSM model can be used for managing risks, evaluation of the options, creating an efficient portfolio.