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A dynamic copula approach to recovering the index implied volatility skew

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  • Matthias Fengler

    ()

  • Helmut Herwartz

    ()

  • Christian Werner

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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.

Suggested Citation

  • Matthias Fengler & Helmut Herwartz & Christian Werner, 2010. "A dynamic copula approach to recovering the index implied volatility skew," University of St. Gallen Department of Economics working paper series 2010 1132, Department of Economics, University of St. Gallen, revised Nov 2011.
    • Handle: RePEc:usg:dp2010:2010-33
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    Cited by:

    1. Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, vol. 30(1), pages 78-98.
    2. Herwartz, Helmut & Raters, Fabian H.C., 2015. "Copula-MGARCH with continuous covariance decomposition," Economics Letters, Elsevier, vol. 133(C), pages 73-76.
    3. Saldías, Martín, 2013. "Systemic risk analysis using forward-looking Distance-to-Default series," Journal of Financial Stability, Elsevier, vol. 9(4), pages 498-517.
    4. repec:bor:bistre:v:17:y:2017:i:1:p:25-48 is not listed on IDEAS
    5. Matthias R. Fengler & Alexander Melnikov, 2018. "GARCH option pricing models with Meixner innovations," Review of Derivatives Research, Springer, vol. 21(3), pages 277-305, October.
    6. 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).

    More about this item

    Keywords

    Copula Dynamic Conditional Correlation; Basket Options; Multivariate GARCH Models; Change of Measure; Esscher Transform;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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