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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

    ()

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.

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Paper provided by Department of Economics, University of St. Gallen in its series University of St. Gallen Department of Economics working paper series 2010 with number 1132.

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Length: 57 pages
Date of creation: Dec 2010
Date of revision: Nov 2011
Handle: RePEc:usg:dp2010:2010-33
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Keywords: Copula Dynamic Conditional Correlation; Basket Options; Multivariate GARCH Models; Change of Measure; Esscher Transform;

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Find related papers by 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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Cited by:

  1. Jeroen Rombouts & Lars Peter Stentoft & Francesco Violente, 2012. "The Value of Multivariate Model Sophistication: An Application to pricing Dow Jones Industrial Average Options," CIRANO Working Papers 2012s-05, CIRANO.
  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 2013/17, Center for Financial Studies (CFS).
  3. Martín Saldías, 2012. "Systemic Risk Analysis using Forward-Looking Distance-to-Default Series," Working Papers w201216, Banco de Portugal, Economics and Research Department.

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