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A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew

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  • Matthias R. Fengler
  • Helmut Herwartz
  • Christian Werner

Abstract

Equity index implied volatility functions are known to be excessively skewed in comparison with implied volatility at the single stock level. We study this stylized fact for the case of a major German stock index, the DAX, by recovering index implied volatility from simulating the 30-dimensional return system of all DAX constituents. Option prices are computed after risk neutralization of the multivariate process which is estimated under the physical probability measure. The multivariate models belong to the class of copula asymmetric dynamic conditional correlation models. We show that moderate tail dependence coupled with asymmetric correlation response to negative news is essential to explain the index implied volatility skew. Standard dynamic correlation models with zero tail dependence fail to generate a sufficiently steep implied volatility skew. Copyright The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

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Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 10 (2012)
Issue (Month): 3 (June)
Pages: 457-493

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Handle: RePEc:oup:jfinec:v:10:y:2012:i:3:p:457-493

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Rombouts, Jeroen V.K. & Stentoft, Lars, 2011. "Multivariate option pricing with time varying volatility and correlations," Journal of Banking & Finance, Elsevier, Elsevier, vol. 35(9), pages 2267-2281, September.
  2. Enzo Giacomini & Wolfgang Härdle & Ekaterina Ignatieva & Vladimir Spokoiny, 2006. "Inhomogeneous Dependency Modelling with Time Varying Copulae," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2006-075, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Nicole Branger & Christian Schlag, 2004. "Why is the Index Smile So Steep?," Review of Finance, Springer, Springer, vol. 8(1), pages 109-127.
  4. Giovannini, Alberto & Jorion, Philippe, 1989. " The Time Variation of Risk and Return in the Foreign Exchange and Stock Markets," Journal of Finance, American Finance Association, American Finance Association, vol. 44(2), pages 307-25, June.
  5. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 57(1), pages 369-403, 02.
  6. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, INFORMS, vol. 44(9), pages 1218-1233, September.
  7. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  8. Drew Creal & Siem Jan Koopman & Andr� Lucas, 2010. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Tinbergen Institute Discussion Papers, Tinbergen Institute 10-032/2, Tinbergen Institute.
  9. René Garcia & Éric Renault, 1997. "A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models," CIRANO Working Papers, CIRANO 97s-13, CIRANO.
  10. Monfort, Alain & Pegoraro, Fulvio, 2012. "Asset pricing with Second-Order Esscher Transforms," Journal of Banking & Finance, Elsevier, Elsevier, vol. 36(6), pages 1678-1687.
  11. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  12. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, INFORMS, vol. 50(9), pages 1204-1221, September.
  13. Fantazzini, Dean, 2009. "The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 53(6), pages 2168-2188, April.
  14. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," Journal of Financial Econometrics, Society for Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 407-458, Fall.
  15. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  16. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers, Warwick Business School, Finance Group wp04-04, Warwick Business School, Finance Group.
  17. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  18. Mo, Henry & Wu, Liuren, 2007. "International capital asset pricing: Evidence from options," Journal of Empirical Finance, Elsevier, Elsevier, vol. 14(4), pages 465-498, September.
  19. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, Elsevier, vol. 97(1), pages 130-154, July.
  20. Sheppard, Kevin & Cappiello, Lorenzo & Engle, Robert F., 2003. "Asymmetric dynamics in the correlations of global equity and bond returns," Working Paper Series, European Central Bank 0204, European Central Bank.
  21. Y. Peter Chung & Michael J. Schill, 2006. "Asset Pricing When Returns Are Nonnormal: Fama-French Factors versus Higher-Order Systematic Comoments," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 79(2), pages 923-940, March.
  22. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2009. "Option Valuation with Conditional Heteroskedasticity and Non-Normality," CIRANO Working Papers, CIRANO 2009s-32, CIRANO.
  23. Christian Schlag & Nicole Branger, 2004. "Why is the index smile so steep?," Money Macro and Finance (MMF) Research Group Conference 2003, Money Macro and Finance Research Group 84, Money Macro and Finance Research Group.
  24. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 19(3), pages 425-442, 09.
  25. Friedrich Hubalek & Carlo Sgarra, 2006. "Esscher transforms and the minimal entropy martingale measure for exponential Levy models," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 6(2), pages 125-145.
  26. Daniel Berg, 2009. "Copula goodness-of-fit testing: an overview and power comparison," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 15(7-8), pages 675-701.
  27. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers, University of California at Berkeley RPF-232, University of California at Berkeley.
  28. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, Elsevier, vol. 131(1-2), pages 253-284.
  29. Pesaran, M. Hashem & Smith, Ron, 1995. "Estimating long-run relationships from dynamic heterogeneous panels," Journal of Econometrics, Elsevier, Elsevier, vol. 68(1), pages 79-113, July.
  30. Timo Terasvirta & Clive W.J Granger & Andrew Patton, 2003. "Common factors in conditional distributions for Bivariate time series," FMG Discussion Papers, Financial Markets Group dp455, Financial Markets Group.
  31. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(3), pages 279-302.
  32. Lee, Tae-Hwy & Long, Xiangdong, 2009. "Copula-based multivariate GARCH model with uncorrelated dependent errors," Journal of Econometrics, Elsevier, Elsevier, vol. 150(2), pages 207-218, June.
  33. Nicolas P. B. Bollen & Robert E. Whaley, 2004. "Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?," Journal of Finance, American Finance Association, American Finance Association, vol. 59(2), pages 711-753, 04.
  34. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, American Finance Association, vol. 49(3), pages 771-818, July.
  35. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, Elsevier, vol. 95(2), pages 391-413, April.
  36. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 289-311.
  37. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, Elsevier, vol. 63(3), pages 443-494, March.
  38. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(1), pages 13-32.
  39. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, Elsevier, vol. 94(1-2), pages 181-238.
  40. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  41. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
  42. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
  43. Joost Driessen & Pascal J. Maenhout & Grigory Vilkov, 2009. "The Price of Correlation Risk: Evidence from Equity Options," Journal of Finance, American Finance Association, American Finance Association, vol. 64(3), pages 1377-1406, 06.
  44. Denis Pelletier, 2004. "Regime Switching for Dynamic Correlations," Econometric Society 2004 North American Summer Meetings, Econometric Society 230, Econometric Society.
  45. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(6), pages 591-604.
  46. van den Goorbergh, Rob W.J. & Genest, Christian & Werker, Bas J.M., 2005. "Bivariate option pricing using dynamic copula models," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 101-114, August.
  47. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 20(3), pages 381-408, June.
  48. Monoyios, Michael, 2007. "The minimal entropy measure and an Esscher transform in an incomplete market model," Statistics & Probability Letters, Elsevier, Elsevier, vol. 77(11), pages 1070-1076, June.
  49. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
  50. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 19(1), pages 3-29, September.
  51. Gunky Kim & Mervyn J. Silvapulle & Paramsothy Silvapulle, 2007. "Estimating the Error Distribution in the Multivariate Heteroscedastic Time Series Models," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 8/07, Monash University, Department of Econometrics and Business Statistics.
  52. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 391-407, March.
  53. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers, CIRANO 95s-43, CIRANO.
  54. Pandu Tadikamalla, 1980. "On simulating non-normal distributions," Psychometrika, Springer, Springer, vol. 45(2), pages 273-279, June.
  55. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, Springer, vol. 6(4), pages 397-428.
  56. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 58(3), pages 1269-1300, 06.
  57. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 72(3), pages 498-505, August.
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Cited by:
  1. Martin Saldías Zambrana, 2010. "Systemic risk analysis using forward-looking distance-to-default series," Working Paper, Federal Reserve Bank of Cleveland 1005, Federal Reserve Bank of Cleveland.
  2. 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, Center for Financial Studies (CFS) 2013/17, Center for Financial Studies (CFS).
  3. Jeroen V.K. Rombouts & Lars Stentoft & Francesco Violante, 2012. "The Value of Multivariate Model Sophistication: An Application to pricing Dow Jones Industrial Average options," CREATES Research Papers, School of Economics and Management, University of Aarhus 2012-04, School of Economics and Management, University of Aarhus.

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