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The Effect of the Hurst Parameter on Value at Risk Estimation in Fractional Geometric Brownian motion Price Simulation

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  • Tendayi Matina

    (University of Zimbabwe, Mathematics and Computational Sciences Department, Harare, Zimbabwe)

  • Edmore Mangwende

    (University of Zimbabwe, Mathematics and Computational Sciences Department, Harare, Zimbabwe)

Abstract

This study assessed the impact of the Hurst parameter on the accuracy of Value at Risk (VaR) estimation using fractional Geometric Brownian motion (fGBM) for stock price simulation. The fGBM model, known for its ability to capture long-term memory in financial time series, was employed to simulate stock prices with varying Hurst parameters. The accuracy of VaR estimations obtained from these simulations was then assessed using mean absolute error metric. The research findings revealed that the Hurst parameter significantly influences the accuracy of VaR estimation in fGBM models. The study identified 0.7 as the optimal Hurst parameter value that enhances VaR estimation accuracy, highlighting the importance of incorporating long-term memory effects in risk assessment. The insights have practical implications for investors and financial institutions seeking to enhance risk management practices. The researchers recommended further researches using different levels of Hurst parameters and VaR at different significant levels.

Suggested Citation

  • Tendayi Matina & Edmore Mangwende, 2024. "The Effect of the Hurst Parameter on Value at Risk Estimation in Fractional Geometric Brownian motion Price Simulation," International Journal of Research and Innovation in Social Science, International Journal of Research and Innovation in Social Science (IJRISS), vol. 8(12), pages 1849-1857, December.
    • Handle: RePEc:bcp:journl:v:8:y:2024:i:12:p:1849-1857
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    1. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    2. Lee, Min-Ku & Yang, Sung-Jin & Kim, Jeong-Hoon, 2016. "A closed form solution for vulnerable options with Heston’s stochastic volatility," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 23-27.
    3. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
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