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Maturity cycles in implied volatility

Author

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  • Jean-Pierre Fouque
  • George Papanicolaou
  • Ronnie Sircar
  • Knut Solna

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

Suggested Citation

  • Jean-Pierre Fouque & George Papanicolaou & Ronnie Sircar & Knut Solna, 2004. "Maturity cycles in implied volatility," Finance and Stochastics, Springer, vol. 8(4), pages 451-477, November.
    • Handle: RePEc:spr:finsto:v:8:y:2004:i:4:p:451-477
    DOI: 10.1007/s00780-004-0126-7
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    Citations

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    Cited by:

    1. Siddiqi, Hammad, 2014. "Analogy Making and the Structure of Implied Volatility Skew," MPRA Paper 60921, University Library of Munich, Germany.
    2. Siddiqi, Hammad, 2013. "Analogy Making in Complete and incomplete Markets: A New Model for Pricing Contingent Claims," Risk and Sustainable Management Group Working Papers 160608, University of Queensland, School of Economics.
    3. Siddiqi, Hammad, 2015. "Anchoring Heuristic in Option Pricing," Risk and Sustainable Management Group Working Papers 207677, University of Queensland, School of Economics.
    4. Jean-Pierre Fouque & Yuri F. Saporito & Jorge P. Zubelli, 2013. "Multiscale Stochastic Volatility Model for Derivatives on Futures," Papers 1311.4249, arXiv.org.
    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. Elisa Alòs & Jorge A. León, 2021. "An Intuitive Introduction to Fractional and Rough Volatilities," Mathematics, MDPI, vol. 9(9), pages 1-22, April.
    7. Siddiqi, Hammad, 2013. "Analogy Making In Complete and Incomplete Markets: A New Model for Pricing Contingent Claims," Risk and Sustainable Management Group Working Papers 156934, University of Queensland, School of Economics.
    8. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    9. Giulia Di Nunno & Kęstutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From Constant to Rough: A Survey of Continuous Volatility Modeling," Mathematics, MDPI, vol. 11(19), pages 1-35, October.
    10. Carlos Fuertes & Andrew Papanicolaou, 2012. "Implied Filtering Densities on Volatility's Hidden State," Papers 1203.6631, arXiv.org, revised Mar 2017.
    11. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    12. Romain Bompis & Emmanuel Gobet, 2012. "Asymptotic and non asymptotic approximations for option valuation," Post-Print hal-00720650, HAL.
    13. 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.
    14. J.-P. Fouque & Y. F. Saporito, 2018. "Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 1003-1016, June.
    15. Siddiqi, Hammad, 2014. "Anchoring Heuristic in Option Prices," MPRA Paper 66018, University Library of Munich, Germany, revised 15 Jul 2015.
    16. Masaaki Fukasawa, 2015. "Short-time at-the-money skew and rough fractional volatility," Papers 1501.06980, arXiv.org.
    17. Siddiqi, Hammad, 2014. "Analogy Making and the Structure of Implied Volatility Skew," Risk and Sustainable Management Group Working Papers 187407, University of Queensland, School of Economics.
    18. Siddiqi, Hammad, 2015. "Anchoring and Adjustment Heuristic in Option Pricing," MPRA Paper 68595, University Library of Munich, Germany.
    19. Elisa Alòs & Jorge A. León & Josep Vives, 2006. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Economics Working Papers 968, Department of Economics and Business, Universitat Pompeu Fabra.
    20. Siddiqi, Hammad, 2014. "Analogy Making and the Puzzles of Index Option Returns and Implied Volatility Skew: Theory and Empirical Evidence," Risk and Sustainable Management Group Working Papers 177302, University of Queensland, School of Economics.
    21. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org.
    22. 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.
    23. Siddiqi, Hammad, 2015. "Anchoring Heuristic in Option Pricing," MPRA Paper 63218, University Library of Munich, Germany.
    24. Kazuki Nagashima & Tsz-Kin Chung & Keiichi Tanaka, 2014. "Asymptotic Expansion Formula of Option Price Under Multifactor Heston Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 351-396, November.

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