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Why is the index smile so steep?

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  • Christian Schlag
  • Nicole Branger

Abstract

Empirical evidence shows that the implied volatility smiles for index options are significantly steeper than those for individual options. We propose a model setup where we start from the joint dynamics of the stocks and where the index value is a weighted sum of individual stock prices. Then the differences between the index smile and the smiles for individual stocks are entirely determined by the dependence structure among the stocks. We illustrate our idea in a jump-diffusion framework where both the diffusion and the jumps are decomposed into common and idiosyncratic components. Empirical data for options on the German stock index DAX and on Deutsche Bank are used to show that the model can explain the stylized facts on implied volatility smiles.
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Suggested Citation

  • Christian Schlag & Nicole Branger, 2004. "Why is the index smile so steep?," Money Macro and Finance (MMF) Research Group Conference 2003 84, Money Macro and Finance Research Group.
    • Handle: RePEc:mmf:mmfc03:84
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    References listed on IDEAS

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    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    2. Berk, Jonathan B, 1995. "A Critique of Size-Related Anomalies," The Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 275-286.
    3. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    4. 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.
    5. Kofman, Paul & Koedijk, Kees & Campbell, Rachel, 2002. "Increased Correlation in Bear markets: A Downside Risk Perspective," CEPR Discussion Papers 3172, C.E.P.R. Discussion Papers.
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    Citations

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    Cited by:

    1. Antoine Jacquier & Saad Slaoui, 2007. "Variance Dispersion and Correlation Swaps," Birkbeck Working Papers in Economics and Finance 0712, Birkbeck, Department of Economics, Mathematics & Statistics.
    2. Shuonan Yuan & Marc Oliver Rieger, 2021. "Diversification with options and structured products," Review of Derivatives Research, Springer, vol. 24(1), pages 55-77, April.
    3. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    4. Félix, Luiz & Kräussl, Roman & Stork, Philip, 2013. "The 2011 European short sale ban on financial stocks: A cure or a curse?," CFS Working Paper Series 2013/17, Center for Financial Studies (CFS).
    5. Dimos S. Kambouroudis & David G. McMillan & Katerina Tsakou, 2021. "Forecasting realized volatility: The role of implied volatility, leverage effect, overnight returns, and volatility of realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(10), pages 1618-1639, October.
    6. Leonidas Tsiaras, 2010. "Dynamic Models of Exchange Rate Dependence Using Option Prices and Historical Returns," CREATES Research Papers 2010-35, Department of Economics and Business Economics, Aarhus University.
    7. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, January.
    8. A. W. Rathgeber & J. Stadler & S. Stöckl, 2021. "The impact of the leverage effect on the implied volatility smile: evidence for the German option market," Review of Derivatives Research, Springer, vol. 24(2), pages 95-133, July.
    9. Lech A. Grzelak & Juliusz Jablecki & Dariusz Gatarek, 2022. "Efficient Pricing and Calibration of High-Dimensional Basket Options," Papers 2206.09877, arXiv.org.
    10. Tzang, Shyh-Weir & Wang, Chou-Wen & Yu, Min-Teh, 2016. "Systematic risk and volatility skew," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 72-87.
    11. Nicola F. Zaugg & Lech A. Grzelak, 2024. "Basket Options with Volatility Skew: Calibrating a Local Volatility Model by Sample Rearrangement," Papers 2407.02901, arXiv.org.
    12. Benjamin Jourdain & Mohamed Sbai, 2012. "Coupling index and stocks," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 805-818, March.
    13. José Da Fonseca & Katrin Gottschalk, 2020. "The Co‐Movement of Credit Default Swap Spreads, Equity Returns and Volatility: Evidence from Asia‐Pacific Markets," International Review of Finance, International Review of Finance Ltd., vol. 20(3), pages 551-579, September.
    14. Ulze, Markus & Stadler, Johannes & Rathgeber, Andreas W., 2021. "No country for old distributions? On the comparison of implied option parameters between the Brownian motion and variance gamma process," The Quarterly Review of Economics and Finance, Elsevier, vol. 82(C), pages 163-184.

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    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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