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On The Relationship Between The Call Price Surface And The Implied Volatility Surface Close To Expiry

  • MICHAEL ROPER

    ()

    (School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia)

  • MAREK RUTKOWSKI

    ()

    (School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia)

Registered author(s):

    We examine the asymptotic behaviour of the call price surface and the associated Black-Scholes implied volatility surface in the small time to expiry limit under the condition of no arbitrage. In the final section, we examine a related question of existence of a market model with non-convergent implied volatility. We show that there exist arbitrage free markets in which implied volatility may fail to converge to any value, finite or infinite.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 12 (2009)
    Issue (Month): 04 ()
    Pages: 427-441

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    Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:04:p:427-441
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    1. Brace, Alan & Fabbri, Giorgio & Goldys, Benjamin, 2007. "An Hilbert space approach for a class of arbitrage free implied volatilities models," MPRA Paper 6321, University Library of Munich, Germany.
    2. Corrado, Charles J. & Miller, Thomas Jr., 1996. "A note on a simple, accurate formula to compute implied standard deviations," Journal of Banking & Finance, Elsevier, vol. 20(3), pages 595-603, April.
    3. 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 637-54, May-June.
    4. Chambers, Donald R & Nawalkha, Sanjay K, 2001. "An Improved Approach to Computing Implied Volatility," The Financial Review, Eastern Finance Association, vol. 36(3), pages 89-99, August.
    5. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
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