A dynamic copula approach to recovering the index implied volatility skew
AbstractEquity 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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Bibliographic InfoPaper 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.
Length: 57 pages
Date of creation: Dec 2010
Date of revision: Nov 2011
Copula Dynamic Conditional Correlation; Basket Options; Multivariate GARCH Models; Change of Measure; Esscher Transform;
Other versions of this item:
- Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-01-16 (All new papers)
- NEP-ECM-2011-01-16 (Econometrics)
- NEP-ORE-2011-01-16 (Operations Research)
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