Conditional Volatility, Skewness, and Kurtosis: Existence and Persistence

56 Pages Posted: 27 Dec 2010

See all articles by Eric Jondeau

Eric Jondeau

University of Lausanne - Faculty of Business and Economics (HEC Lausanne); Swiss Finance Institute

Michael Rockinger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne); Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Multiple version iconThere are 2 versions of this paper

Date Written: November 2000

Abstract

Recent portfolio choice asset pricing and option valuation models highlight the importance of skewness and kurtosis. Since skewness and kurtosis are related to extreme variations they are also important for Value-at-Risk measurements. Our framework builds on a GARCH model with a condi-tional generalized-t distribution for residuals. We compute the skewness and kurtosis for this model and compare the range of these moments with the maximal theoretical moments. Our model thus allows for time-varying conditional skewness and kurtosis. We implement the model as a constrained optimization with possibly several thousand restrictions on the dynamics. sequential quadratic programming algorithm successfully estimates all the models on a PC within at most 50 seconds. Estimators obtained with logistically-constrained dynamics have different properties. We apply this model to daily and weekly foreign exchange returns stock returns and interest-rate changes. We show that skewness exists for many dates and for almost all series except short-term interest-rate changes. This finding is consistent with findings from extreme value theory. Kurtosis exists on fewer dates and for fewer series. There is little evidence at the weekly frequency of time-variability of conditional higher moments. Transition matrices document that agitated states come as a surprise and that there is a certain persistence in moments beyond volatility. For exchange-rate and stock-market data cross-sectionally and at daily frequency we also document co-variability of moments beyond volatility.

Keywords: GRCH, Stock indices, Exchange rates, Interest rates, SNOPT VaR

JEL Classification: C22, C51, G12

Suggested Citation

Jondeau, Eric and Rockinger, Georg Michael, Conditional Volatility, Skewness, and Kurtosis: Existence and Persistence (November 2000). Banque de France Working Paper No. 77. Available at SSRN: https://ssrn.com/abstract=1730591 or http://dx.doi.org/10.2139/ssrn.1730591

Eric Jondeau (Contact Author)

University of Lausanne - Faculty of Business and Economics (HEC Lausanne) ( email )

Extranef 232
Lausanne, 1012
Switzerland
+41 21 692 33 49 (Phone)

HOME PAGE: http://www.hec.unil.ch/ejondeau/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Georg Michael Rockinger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Internef
Lausanne, 1015
Switzerland
+41 21 728 3348 (Phone)
+41+21 692 3435 (Fax)

HOME PAGE: http://www.hec.unil.ch/mrockinger

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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