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Simple Formulas to Option Pricing and Hedging in the Black- Scholes Model


  • paolo pianca

    (Dipartimento di Matematica Applicata Università di Venezia)


For option whose striking price equals the forward price of the underlying asset, the Black-Scholes pricing formula can be approximated in closed-form. A interesting result is that the derived equation is not only very simple in structure but also that it can be immediately inverted to obtain an explicit formula for implied volatility. In this contribution we present and compare the accuracy of three of such approximation formulas. The numerical analysis shows that the first order approximations are close only for small maturities, Polya approximations are remarkably accurate for a very large range of parameters, while logistic values are the most accurate only for extreme maturities.

Suggested Citation

  • paolo pianca, 2005. "Simple Formulas to Option Pricing and Hedging in the Black- Scholes Model," Finance 0511005, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpfi:0511005
    Note: Type of Document - pdf; pages: 9

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    References listed on IDEAS

    1. 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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    Cited by:

    1. Michael R. Tehranchi, 2015. "Uniform bounds for Black--Scholes implied volatility," Papers 1512.06812,, revised Aug 2016.
    2. Ahmadian, D. & Farkhondeh Rouz, O. & Ivaz, K. & Safdari-Vaighani, A., 2020. "Robust numerical algorithm to the European option with illiquid markets," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    3. Dan Stefanica & Radoš Radoičić, 2017. "An Explicit Implied Volatility Formula," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-32, November.
    4. Michele Mininni & Giuseppe Orlando & Giovanni Taglialatela, 2018. "Challenges in approximating the Black and Scholes call formula with hyperbolic tangents," Papers 1810.04623,
    5. Dan Stefanica & Radoš Radoičić, 2016. "A sharp approximation for ATM-forward option prices and implied volatilites," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-24, March.

    More about this item


    Option pricing; hedging; Taylor; Polya and logistic approximations;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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