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On the Numerical Option Pricing Methods: Fractional Black-Scholes Equations with CEV Assets

Author

Listed:
  • S. Banihashemi

    (University of Mazandaran)

  • A. Ghasemifard

    (University of Mazandaran)

  • A. Babaei

    (University of Mazandaran)

Abstract

This article explores a stochastic volatility model that incorporates fractional Brownian motion (fBm) into the constant elasticity of variance (CEV) framework. We use time series models to estimate the drift and volatility parameters of the model and validate its performance. We also examine the fractional Black-Scholes (BS) equation arising from the CEV model with fBm. To solve this equation numerically, we apply a Chebyshev collocation method and analyze its convergence properties. We demonstrate the effectiveness of the numerical method with an example and apply it to the option pricing problem.

Suggested Citation

  • S. Banihashemi & A. Ghasemifard & A. Babaei, 2024. "On the Numerical Option Pricing Methods: Fractional Black-Scholes Equations with CEV Assets," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1463-1488, September.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:3:d:10.1007_s10614-023-10482-4
    DOI: 10.1007/s10614-023-10482-4
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    References listed on IDEAS

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    1. Beckers, Stan, 1980. "The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    3. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    4. Tomas Björk & Henrik Hult, 2005. "A note on Wick products and the fractional Black-Scholes model," Finance and Stochastics, Springer, vol. 9(2), pages 197-209, April.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Álvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.
    7. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Haq, Sirajul & Hussain, Manzoor, 2018. "Selection of shape parameter in radial basis functions for solution of time-fractional Black–Scholes models," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 248-263.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Jumarie, Guy, 2008. "Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 271-287, February.
    11. Hossein Jafari & Afshin Babaei & Seddigheh Banihashemi, 2019. "A Novel Approach for Solving an Inverse Reaction–Diffusion–Convection Problem," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 688-704, November.
    12. José Carlos Dias & João Pedro Vidal Nunes, 2011. "Pricing real options under the constant elasticity of variance diffusion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(3), pages 230-250, March.
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