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

"Using Modified Multifractal MMAR Model for Predicting Financial Data Volatility"

Accomplished by P.A. Valinevich
Supervised by L.A. Dmitrieva

The main goal of this work was modification of the MMAR (Multifractal Model of Asset Returns) model created by B. Mandelbrot. The aim was to add casualty characteristics to it thus making it suitable for predicting financial time series volatility. The idea of modification proposed in this work lies in bringing the MMAR model to conditionally Gaussian models and changing the multifractal measure which determines volatility. In particular instead of the classical multiplicative measure the conservative measure was used. After that it was shown that the modified model reproduces many of characteristics inherent to the real financial time series, such as multyfractality, volatility clusterization, thick tails and sharp peaks in the yield distribution, and long volatility memory. Modified model provides an opportunity for building one-step volatility forecasts which cannot be done using MMAR. For a number of the US shares and stock market indices the forecasts built on the basis of the elaborated model were compared to the ones built on the basis of the GARCH reference model. It was shown that the forecasts of the modified MMAR model are not worse and sometimes even more accurate than those built on the basis of GARCH. Apart form that it was shown that the modified MMAR model forecasts in all examined cases were statistically better than the ones build on the basis of the historical volatility. The research also includes the comparison of the modified MMAR model with the GARCH model from the point of view of the Value-at-Risk forecast.