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Volatility surfaces: theory, rules of thumb, and empirical evidence

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  • Toby Daglish
  • John Hull
  • Wulin Suo

Abstract

Implied volatilities are frequently used to quote the prices of options. The implied volatility of a European option on a particular asset as a function of strike price and time to maturity is known as the asset's volatility surface. Traders monitor movements in volatility surfaces closely. In this paper we develop a no-arbitrage condition for the evolution of a volatility surface. We examine a number of rules of thumb used by traders to manage the volatility surface and test whether they are consistent with the no-arbitrage condition and with data on the trading of options on the S&P 500 taken from the over-the-counter market. Finally we estimate the factors driving the volatility surface in a way that is consistent with the no-arbitrage condition.

Suggested Citation

  • Toby Daglish & John Hull & Wulin Suo, 2007. "Volatility surfaces: theory, rules of thumb, and empirical evidence," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 507-524.
    • Handle: RePEc:taf:quantf:v:7:y:2007:i:5:p:507-524
    DOI: 10.1080/14697680601087883
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    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    3. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Hull, John & Suo, Wulin, 2002. "A Methodology for Assessing Model Risk and its Application to the Implied Volatility Function Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(2), pages 297-318, June.
    6. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    7. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    9. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    10. Rama Cont & Jose da Fonseca & Valdo Durrleman, 2002. "Stochastic Models of Implied Volatility Surfaces," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 361-377, July.
    11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    12. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    13. 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.
    14. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    15. P. Balland, 2002. "Deterministic implied volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 31-44.
    16. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

    1. Pascal François & Lars Stentoft, 2021. "Smile‐implied hedging with volatility risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(8), pages 1220-1240, August.
    2. Wang, Ximei & Zhao, Yanlong & Bao, Ying, 2019. "Arbitrage-free conditions for implied volatility surface by Delta," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 819-834.
    3. repec:hum:wpaper:sfb649dp2005-020 is not listed on IDEAS
    4. Shiva Zamani & Alireza Moslemi Haghighi & Hamid Arian, 2023. "Temporal Volatility Surface Projection: Parametric Surface Projection Method for Derivatives Portfolio Risk Management," Papers 2311.14985, arXiv.org.
    5. Frédéric Abergel & Riadh Zaatour, 2012. "What drives option prices ?," Post-Print hal-00687675, HAL.
    6. Carey, Alexander, 2010. "Higher-order volatility: time series," MPRA Paper 21087, University Library of Munich, Germany.
    7. Fengler, Matthias R. & Härdle, Wolfgang Karl & Mammen, Enno, 2005. "A dynamic semiparametric factor model for implied volatility string dynamics," SFB 649 Discussion Papers 2005-020, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. F. Leung & M. Law & S. K. Djeng, 2024. "Deterministic modelling of implied volatility in cryptocurrency options with underlying multiple resolution momentum indicator and non-linear machine learning regression algorithm," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-25, December.
    9. Amine Bouden, 2008. "The Behavior Of The Implied Volatility Surface: Evidence From Crude Oil Futures Options," World Scientific Book Chapters, in: Mondher Bellalah & Jean-Luc Prigent & Jean-Michel Sahut & Georges Pariente & Olivier Levyne & Michel (ed.), Risk Management And Value Valuation and Asset Pricing, chapter 8, pages 151-175, World Scientific Publishing Co. Pte. Ltd..
    10. repec:hal:wpaper:hal-00687675 is not listed on IDEAS
    11. Claude Martini & Iacopo Raffaelli, 2021. "Revisiting the Implied Remaining Variance framework of Carr and Sun (2014): Locally consistent dynamics and sandwiched martingales," Papers 2105.06390, arXiv.org.
    12. Pascal François & Rémi Galarneau‐Vincent & Geneviève Gauthier & Frédéric Godin, 2022. "Venturing into uncharted territory: An extensible implied volatility surface model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1912-1940, October.
    13. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2021. "Arbitrage-free neural-SDE market models," Papers 2105.11053, arXiv.org, revised Aug 2021.
    14. Wang, Jinzhong & Chen, Shijiang & Tao, Qizhi & Zhang, Ting, 2017. "Modelling the implied volatility surface based on Shanghai 50ETF options," Economic Modelling, Elsevier, vol. 64(C), pages 295-301.
    15. Jacinto Marabel Romo, 2012. "Volatility Regimes For The Vix Index," Revista de Economia Aplicada, Universidad de Zaragoza, Departamento de Estructura Economica y Economia Publica, vol. 20(2), pages 111-134, Autumn.
    16. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    17. Itkin, Andrey, 2015. "To sigmoid-based functional description of the volatility smile," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 264-291.
    18. Peter Carr & Liuren Wu, 2020. "Option Profit and Loss Attribution and Pricing: A New Framework," Journal of Finance, American Finance Association, vol. 75(4), pages 2271-2316, August.
    19. Carr, Peter & Wu, Liuren, 2016. "Analyzing volatility risk and risk premium in option contracts: A new theory," Journal of Financial Economics, Elsevier, vol. 120(1), pages 1-20.
    20. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    21. Wallmeier, Martin, 2012. "Smile in Motion: An Intraday Analysis of Asymmetric Implied Volatility," FSES Working Papers 427, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    22. Xin‐Jiang He & Song‐Ping Zhu, 2018. "On full calibration of hybrid local volatility and regime‐switching models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(5), pages 586-606, May.

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