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Maturity cycles in implied volatility

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Author Info

  • Jean-Pierre Fouque

    ()

  • George Papanicolaou

    ()

  • Ronnie Sircar

    ()

  • Knut Solna

    ()

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    Abstract

    The skew effect in market implied volatility can be reproduced by option pricing theory based on stochastic volatility models for the price of the underlying asset. Here we study the performance of the calibration of the S&P 500 implied volatility surface using the asymptotic pricing theory under fast mean-reverting stochastic volatility described in [8]. The time-variation of the fitted skew-slope parameter shows a periodic behaviour that depends on the option maturity dates in the future, which are known in advance. By extending the mathematical analysis to incorporate model parameters which are time-varying, we show this behaviour can be explained in a manner consistent with a large model class for the underlying price dynamics with time-periodic volatility coefficients. Copyright Springer-Verlag Berlin/Heidelberg 2004

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    File URL: http://hdl.handle.net/10.1007/s00780-004-0126-7
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 8 (2004)
    Issue (Month): 4 (November)
    Pages: 451-477

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    Handle: RePEc:spr:finsto:v:8:y:2004:i:4:p:451-477

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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Implied volatilities; maturity cycles; fast mean-reverting stochastic volatility; asymptotic expansions;

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    Cited by:
    1. Jean-Pierre Fouque & Yuri F. Saporito & Jorge P. Zubelli, 2013. "Multiscale Stochastic Volatility Model for Derivatives on Futures," Papers 1311.4249, arXiv.org.
    2. Elisa Alòs & Jorge A. León, 2013. "On the closed-form approximation of short-time random strike options," Economics Working Papers 1347, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Elisa Alòs & Jorge León & Josep Vives, 2007. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Finance and Stochastics, Springer, vol. 11(4), pages 571-589, October.
    4. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    5. Sukhomlin, Nikolay & Santana Jiménez, Lisette Josefina, 2010. "Problema de calibración de mercado y estructura implícita del modelo de bonos de Black-Cox = Market Calibration Problem and the Implied Structure of the Black-Cox Bond Model," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 10(1), pages 73-98, December.
    6. Romain Bompis & Emmanuel Gobet, 2012. "Asymptotic and non asymptotic approximations for option valuation," Post-Print hal-00720650, HAL.

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