Author(s)

Bou Diop

Department of Mathematics and Computer Science, Faculty of Technology and Computer Science, University Iba Der Thiam of Thiès, Thiès, Senegal.

This article proposes an innovative method for modeling financial markets using multifractional Brownian motion (mBm). Unlike traditional fractional Brownian motion, mBm offers variable local memory, providing a more accurate representation of the multifractal volatility and long-range dependencies found in financial time series. We present a precise mathematical formulation of mBm, sophisticated techniques for estimating the Hurst function, efficient numerical simulation algorithms, and a detailed empirical study covering several major stock indices. The results indicate that mBm more accurately reflects price dynamics, significantly improves risk analysis, and provides more precise pricing of exotic options compared to traditional models.

Multifractional Brownian Motion (mBm), Hurst Exponent, Volatility Modeling, Long Memory, Financial Risk, Stochastic Volatility, Value at Risk (VaR), Expected Shortfall (ES), Time-Varying Regularity

Diop, B. (2025) Application of Multifractional Brownian Motion to Modeling Volatility and Risk in Financial Markets. Journal of Applied Mathematics and Physics, 13, 3854-3870. doi: 10.4236/jamp.2025.1311216.