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An Approximation Scheme for Option Pricing Under Two-State Continuous CAPM

Author

Listed:
  • Ali Safdari-Vaighani

    (Allameh Tabataba’i University)

  • Davood Ahmadian

    (University of Tabriz)

  • Roja Javid-Jahromi

    (Shahed University)

Abstract

Option pricing under continuous-time CAPM has been formulated by partial differential equation, which is an extension of the Black–Scholes PDE. The focus of this paper is to present the radial basis function partition of unity method for evaluation of options in which underlying asset price follows the two-state continuous CAPM. Our experiments illustrate the behavior of the market volatility skew and the effect of the asset’s beta on option price. The numerical examples show that the proposed scheme is accurate and competitive with finite difference method.

Suggested Citation

  • Ali Safdari-Vaighani & Davood Ahmadian & Roja Javid-Jahromi, 2021. "An Approximation Scheme for Option Pricing Under Two-State Continuous CAPM," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1373-1385, April.
    • Handle: RePEc:kap:compec:v:57:y:2021:i:4:d:10.1007_s10614-020-10024-2
    DOI: 10.1007/s10614-020-10024-2
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    References listed on IDEAS

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    1. Jean-Pierre Fouque & Eli Kollman, 2011. "Calibration of Stock Betas from Skews of Implied Volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(2), pages 119-137.
    2. Jean-Pierre Fouque & Adam Tashman, 2012. "Option pricing under a stressed-beta model," Annals of Finance, Springer, vol. 8(2), pages 183-203, May.
    3. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    4. 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.
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