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

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  • 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)

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    Abstract

    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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    Bibliographic Info

    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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    Related research

    Keywords: Option pricing; implied volatility; logarithmic limit; Black-Scholes formula; asymptotic and approximate formulae;

    References

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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. 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.
    3. 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.
    4. 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.
    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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    Cited by:
    1. Stefan Gerhold, 2012. "Can there be an explicit formula for implied volatility?," Papers 1211.4978, arXiv.org.
    2. Stefan Gerhold & Ismail Cetin G\"ul\"um, 2013. "The Small Maturity Implied Volatility Slope for L\'evy Models," Papers 1310.3061, arXiv.org, revised Aug 2014.
    3. Kun Gao & Roger Lee, 2014. "Asymptotics of implied volatility to arbitrary order," Finance and Stochastics, Springer, vol. 18(2), pages 349-392, April.
    4. Stefan Gerhold & Max Kleinert & Piet Porkert & Mykhaylo Shkolnikov, 2012. "Small time central limit theorems for semimartingales with applications," Papers 1208.4282, arXiv.org.
    5. Zhi Jun Guo & Eckhard Platen, 2012. "The Small And Large Time Implied Volatilities In The Minimal Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1250057-1-1.
    6. Aleksandar Mijatovi\'c & Peter Tankov, 2012. "A new look at short-term implied volatility in asset price models with jumps," Papers 1207.0843, arXiv.org, revised Jul 2012.

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