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On expansions for the Black-Scholes prices and hedge parameters

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  • Jean-Philippe Aguilar

Abstract

We derive new formulas for the price of the European call and put options in the Black-Scholes model, under the form of uniformly convergent series generalizing previously known approximations. We also provide precise boundaries for the convergence speed and apply the results to the calculation of hedge parameters (Greeks).

Suggested Citation

  • Jean-Philippe Aguilar, 2018. "On expansions for the Black-Scholes prices and hedge parameters," Papers 1809.06736, arXiv.org, revised Jun 2019.
    • Handle: RePEc:arx:papers:1809.06736
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    References listed on IDEAS

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    1. Arturo Estrella, 1995. "Taylor, Black and Scholes: series approximations and risk management pitfalls," Research Paper 9501, Federal Reserve Bank of New York.
    2. 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.
    3. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. Jean-Philippe Aguilar, 2019. "The value of power-related options under spectrally negative L\'evy processes," Papers 1910.07971, arXiv.org, revised Jan 2021.
    2. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.

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