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<p>This study investigates the effectiveness of fractional Brownian motion in modeling and hedging stock price dynamics, compared to standard Brownian motion, using data from the S&amp;P 500 and NYSE across periods surrounding the 2008 financial crisis and the COVID-19 pandemic. We estimate the Hurst exponent via rescaled range analysis to calibrate fractional Brownian-based models and assess predictive accuracy (via Mean Absolute Percentage Error) and hedging performance through Monte Carlo simulations of 1,000 price paths. The results show that fractional Brownian models generally yield better forecasts during crisis periods and provide more stable hedging outcomes-especially when the Hurst exponent <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varvec{H \ge 0.5}\)</EquationSource> </InlineEquation>. Even when forecasting accuracy is similar to Brownian motion, fractional Brownian motion improves risk mitigation by capturing long-range dependence. However, when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varvec{H &lt; 0.5}\)</EquationSource> </InlineEquation>, as seen in the NYSE post-COVID, fractional Brownian motion may increase exposure to tail risk. These findings underscore the need for careful Hurst exponent calibration in memory-sensitive risk management frameworks.</p>

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Dynamic Delta Hedging During Crises: Fractional Brownian Motion in Action

  • 期刊论文

  • 发表日期：

    2025年12月13日

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  • Tamirat Temesgen Dufera,
  • Dakito Alemu Kesto,
  • Tenkir Seifu Legesse

摘要

This study investigates the effectiveness of fractional Brownian motion in modeling and hedging stock price dynamics, compared to standard Brownian motion, using data from the S&P 500 and NYSE across periods surrounding the 2008 financial crisis and the COVID-19 pandemic. We estimate the Hurst exponent via rescaled range analysis to calibrate fractional Brownian-based models and assess predictive accuracy (via Mean Absolute Percentage Error) and hedging performance through Monte Carlo simulations of 1,000 price paths. The results show that fractional Brownian models generally yield better forecasts during crisis periods and provide more stable hedging outcomes-especially when the Hurst exponent \(\varvec{H \ge 0.5}\) . Even when forecasting accuracy is similar to Brownian motion, fractional Brownian motion improves risk mitigation by capturing long-range dependence. However, when \(\varvec{H < 0.5}\) , as seen in the NYSE post-COVID, fractional Brownian motion may increase exposure to tail risk. These findings underscore the need for careful Hurst exponent calibration in memory-sensitive risk management frameworks.