TITLE:
Application of Multifractional Brownian Motion to Modeling Volatility and Risk in Financial Markets
AUTHORS:
Bou Diop
KEYWORDS:
Multifractional Brownian Motion (mBm), Hurst Exponent, Volatility Modeling, Long Memory, Financial Risk, Stochastic Volatility, Value at Risk (VaR), Expected Shortfall (ES), Time-Varying Regularity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
17,
2025
ABSTRACT: 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.