Conditional Volatility, Skewness, and Kurtosis : Existence and Persistence
AbstractRecent 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 conditional 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. A 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. 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 stares 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.
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Bibliographic InfoPaper provided by HEC Paris in its series Les Cahiers de Recherche with number 710.
Length: 48 pages
Date of creation: 01 Jul 2000
Date of revision:
Garch; stock indices; exchange rates; interest rates; SNOPT; VaR;
Other versions of this item:
- Jondeau, E. & Rockinger, M., 2000. "Conditional Volatility, Skewness, and Kurtosis: Existence and Persistence," Working papers 77, Banque de France.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- Gallant, A.R. & Tauchen, G., 1988.
"Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications,"
88-59, Chicago - Graduate School of Business.
- Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
- Hansen, B.E., 1992.
"Autoregressive Conditional Density Estimation,"
RCER Working Papers
322, University of Rochester - Center for Economic Research (RCER).
- Hwang, Soosung & Satchell, Stephen E, 1999.
"Modelling Emerging Market Risk Premia Using Higher Moments,"
International Journal of Finance & Economics,
John Wiley & Sons, Ltd., vol. 4(4), pages 271-96, October.
- Hwang, S. & Satchell, S. E., 1998. "Modelling Emerging Market Risk Premia using Higher Moments," Cambridge Working Papers in Economics 9806, Faculty of Economics, University of Cambridge.
- Stephen Satchell & Soosung Hwang, 1999. "Modelling Emerging Market Risk Premia Using Higher Moments," Working Papers wp99-17, Warwick Business School, Finance Group.
- Raymond Kan & Guofu Zhou, 1999.
"A Critique of the Stochastic Discount Factor Methodology,"
Journal of Finance,
American Finance Association, vol. 54(4), pages 1221-1248, 08.
- Raymond Kan & Guofu Zhou, 1999. "A Critique of the Stochastic Discount Factor Methodology," CEMA Working Papers 12, China Economics and Management Academy, Central University of Finance and Economics.
- Ramchand, Latha & Susmel, Raul, 1998. "Volatility and cross correlation across major stock markets," Journal of Empirical Finance, Elsevier, vol. 5(4), pages 397-416, October.
- Richardson, Matthew & Smith, Tom, 1993. "A Test for Multivariate Normality in Stock Returns," The Journal of Business, University of Chicago Press, vol. 66(2), pages 295-321, April.
- Longin, Francois & Solnik, Bruno, 1995. "Is the correlation in international equity returns constant: 1960-1990?," Journal of International Money and Finance, Elsevier, vol. 14(1), pages 3-26, February.
- Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
- Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993.
" On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1779-1801, December.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
- Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-44.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-28, June.
- Sentana, Enrique, 1995.
"Quadratic ARCH Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 62(4), pages 639-61, October.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Gray, Stephen F., 1996.
"Modeling the conditional distribution of interest rates as a regime-switching process,"
Journal of Financial Economics,
Elsevier, vol. 42(1), pages 27-62, September.
- Tom Doan, . "RATS programs to replicate Gray's 1996 Regime Switching GARCH paper," Statistical Software Components RTZ00080, Boston College Department of Economics.
- Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
- Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
- Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-66, December.
- Tan, Kai-Jiaw, 1991. "Risk return and the three-moment capital asset pricing model: another look," Journal of Banking & Finance, Elsevier, vol. 15(2), pages 449-460, April.
- Susmel, Raul & Engle, Robert F., 1994. "Hourly volatility spillovers between international equity markets," Journal of International Money and Finance, Elsevier, vol. 13(1), pages 3-25, February.
- Sears, R Stephen & Wei, K C John, 1988. "The Structure of Skewness Preferences in Asset Pricing Models with Higher Moments: An Empirical Test," The Financial Review, Eastern Finance Association, vol. 23(1), pages 25-38, February.
- Sears, R Stephen & Wei, K C John, 1985. " Asset Pricing, Higher Moments, and the Market Risk Premium: A Note," Journal of Finance, American Finance Association, vol. 40(4), pages 1251-53, September.
- Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
- Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
- Barone-Adesi, Giovanni, 1985. "Arbitrage Equilibrium with Skewed Asset Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(03), pages 299-313, September.
- ROCKINGER, Michael & JONDEAU, Eric, 2001.
"Conditional dependency of financial series : an application of copulas,"
Les Cahiers de Recherche
723, HEC Paris.
- Rockinger, M. & Jondeau, E., 2001. "Conditional Dependency of Financial Series: An Application of Copulas," Working papers 82, Banque de France.
- Chris Brooks & Simon P. Burke & Gita Persand, 2002.
"Augoregressive Conditional Kurtosis,"
ICMA Centre Discussion Papers in Finance
icma-dp2002-05, Henley Business School, Reading University.
- Andrei Leonidov & Vladimir Trainin & Alexander Zaitsev & Sergey Zaitsev, 2006. "Market Mill Dependence Pattern in the Stock Market: Asymmetry Structure, Nonlinear Correlations and Predictability," Papers physics/0601098, arXiv.org, revised Jan 2006.
- Ángel León & Gonzalo Rubio & Gregorio Serna, 2004. "Autoregressive Conditional Volatility, Skewness And Kurtosis," Working Papers. Serie AD 2004-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Onour, Ibrahim, 2008. "Forward-Looking Beta Estimates:Evidence from an Emerging Market," MPRA Paper 14992, University Library of Munich, Germany.
- Onour, Ibrahim, 2010.
"The Global Financial Crisis and Equity Markets in Middle East Oil Exporting Countries,"
23332, University Library of Munich, Germany.
- Dr. Ibrahim Onour, . "The Global Financial Crisis and Equity Markets in Middle East Oil Exporting Countries," API-Working Paper Series 1009, Arab Planning Institute - Kuwait, Information Center.
- Anthony S. Tay & Aamir R. Hashmi, 2004.
"Global and Regional Sources of Risk in Equity Markets: Evidence from Factor Models with Time-Varying Conditional Skewness,"
Econometric Society 2004 Far Eastern Meetings
634, Econometric Society.
- Aamir R. Hashmi & Anthony S. Tay, 2001. "Global and Regional Sources of Risk in Equity Markets: Evidence from Factor Models with Time-Varying Conditional Skewness," Departmental Working Papers wp0116, National University of Singapore, Department of Economics.
- Tao Pham Dinh & Yi-Shuai Niu, 2011. "An efficient DC programming approach for portfolio decision with higher moments," Computational Optimization and Applications, Springer, vol. 50(3), pages 525-554, December.
- Ibrahim Onour, . "Exploring Stability of Systematic Risk: Sectoral Portfolio Analysis," API-Working Paper Series 1002, Arab Planning Institute - Kuwait, Information Center.
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