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Fractional Brownian motion in option pricing and dynamic delta hedging: Experimental simulations

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  • Dufera, Tamirat Temesgen

Abstract

This research examines the impact of fractional Brownian motion (fBm) on option pricing and dynamic delta hedging. Through experimental simulations, we analyze the influence of the Hurst exponent on option price prediction. Our findings highlight the necessity for continuous calibration of the Hurst exponent for a specific market dataset. By estimating option prices using fBm, we evaluate price prediction accuracy and explore fBm’s benefits in option pricing models. We also investigate dynamic delta hedging strategies for call options within the fBm framework, providing an algorithm and code that consider the Hurst exponent. The study’s insights contribute to advancing financial modeling and risk management practices, illuminating the dynamic nature of market phenomena and underscoring calibration’s significance in capturing market dynamics. The findings emphasize the dynamic interplay between the Hurst exponent and option pricing, offering valuable implications for effective risk management strategies.

Suggested Citation

  • Dufera, Tamirat Temesgen, 2024. "Fractional Brownian motion in option pricing and dynamic delta hedging: Experimental simulations," The North American Journal of Economics and Finance, Elsevier, vol. 69(PB).
    • Handle: RePEc:eee:ecofin:v:69:y:2024:i:pb:s1062940823001407
    DOI: 10.1016/j.najef.2023.102017
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    Keywords

    European options; Fractional Brownian motion; Black–Scholes–Merton model; Dynamic delta hedging; Hurst exponent; Simulation;
    All these keywords.

    JEL classification:

    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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