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A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew

Matthias Fengler, H. 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.
   
type journal paper
   
keywords
   
language English
kind of paper journal article
date of appearance 3-2012
journal Journal of Financial Econometrics
publisher Oxford Journals (Oxford UK)
ISSN 1479-8409
ISSN (online) 1479-8417
DOI 10.1093/jjfinec/nbr016
volume of journal 10
number of issue 3
page(s) 457-493
review double-blind review
   
citation Fengler, M., Herwartz, H., & Werner, C. (2012). A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew. Journal of Financial Econometrics, 10(3), 457-493, DOI:10.1093/jjfinec/nbr016.