Is Volatility Clustering of Asset Returns Asymmetric

Volatility clustering is a well-known stylized feature of financial asset returns. This paper investigates asymmetric pattern in volatility clustering by employing a univariate copula approach of Chen and Fan (2006). Using daily realized kernel volatilities constructed from high frequency data from stock and foreign exchange markets, we find evidence that volatility clustering is highly nonlinear and strongly asymmetric in that clusters of high volatility occur more often than clusters of low volatility. To the best of our knowledge, this paper is the first one to address and uncover this phenomenon. In particular, the asymmetry in volatility clustering is found to be more pronounced in the stock markets than in the foreign exchange markets. Further, the volatility clusters are shown to remain persistent for over a month and asymmetric across different time periods. Our findings have important implications for risk management. A simulation study indicates that models which accommodate asymmetric volatility clustering can significantly improve the out-of-sample forecasts of Value-at-Risk.

[1]  P. Hansen,et al.  Realized Variance and Market Microstructure Noise , 2005 .

[2]  Andrew J. Patton Copula-Based Models for Financial Time Series , 2009 .

[3]  Cathy Ning,et al.  Dependence structure between the equity market and the foreign exchange market–A copula approach , 2010 .

[4]  Ba Chu,et al.  Recovering copulas from limited information and an application to asset allocation , 2011 .

[5]  Joel Hasbrouck,et al.  Assessing the Quality of a Security Market: A New Approach to Transaction-Cost Measurement , 1993 .

[6]  C. Genest,et al.  A semiparametric estimation procedure of dependence parameters in multivariate families of distributions , 1995 .

[7]  Andrew J. Patton Modelling Asymmetric Exchange Rate Dependence , 2006 .

[8]  N. Shephard,et al.  Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics , 2001 .

[9]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[10]  Subu Venkataraman,et al.  Value at risk for a mixture of normal distributions: the use of quasi- Bayesian estimation techniques , 1997 .

[11]  Siem Jan Koopman,et al.  Forecasting Daily Variability of the S&P 100 Stock Index Using Historical, Realised and Implied Volatility Measurements , 2005 .

[12]  J. Tawn,et al.  Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications , 2004 .

[13]  M. Sklar Fonctions de repartition a n dimensions et leurs marges , 1959 .

[14]  Heni Boubaker,et al.  Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach. , 2013 .

[15]  B. Rémillard Goodness-of-Fit Tests for Copulas of Multivariate Time Series , 2010 .

[16]  Michael McAleer,et al.  Realized Volatility: A Review , 2008 .

[17]  Robert F. Engle,et al.  Risk and Volatility: Econometric Models and Financial Practice , 2004 .

[18]  N. Shephard,et al.  Estimating quadratic variation using realized variance , 2002 .

[19]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[20]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[21]  Andrew J. Patton A review of copula models for economic time series , 2012, J. Multivar. Anal..

[22]  P. Hansen,et al.  Realized GARCH: A Joint Model of Returns and Realized Measures of Volatility , 2010 .

[23]  B. Rémillard,et al.  Goodness-of-fit tests for copulas: A review and a power study , 2006 .

[24]  H. Joe Multivariate models and dependence concepts , 1998 .

[25]  Peter F. Christoffersen Evaluating Interval Forecasts , 1998 .

[26]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .

[27]  E. Luciano,et al.  Copula methods in finance , 2004 .

[28]  Thomas H. McCurdy,et al.  Do High-Frequency Measures of Volatility Improve Forecasts of Return Distributions? , 2008 .

[29]  N. Shephard,et al.  Realized Kernels in Practice: Trades and Quotes , 2009 .

[30]  B. Ray,et al.  Long-range Dependence in Daily Stock Volatilities , 2000 .

[31]  D. Dijk,et al.  Measuring volatility with the realized range , 2006 .

[32]  Yi-Chiuan Wang,et al.  A Revisit to the Dependence Structure between Stock and Foreign Exchange Markets: A Dependence-Switching Copula Approach , 2012 .

[33]  Neil Shephard,et al.  Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise , 2008 .

[34]  Jose A. Lopez,et al.  Methods for Evaluating Value-at-Risk Estimates , 1998 .

[35]  F. Diebold,et al.  Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility , 2005, The Review of Economics and Statistics.

[36]  H. Iemoto Modelling the persistence of conditional variances , 1986 .

[37]  R. Nelsen An Introduction to Copulas , 1998 .

[38]  P. Hansen,et al.  A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data , 2005 .

[39]  M. Martens Measuring and Forecasting S&P 500 Index-Futures Volatility Using High-Frequency Data , 2002 .

[40]  Daniel Berg Copula goodness-of-fit testing: an overview and power comparison , 2009 .

[41]  Jamie Alcock,et al.  Canonical Vine Copulas in the Context of Modern Portfolio Management: Are They Worth It? , 2013 .

[42]  V. Peña,et al.  International diversification: A copula approach , 2011 .

[43]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[44]  J. C. Rodríguez,et al.  Measuring financial contagion:a copula approach , 2007 .

[45]  M. Rockinger,et al.  The Copula-GARCH model of conditional dependencies: An international stock market application , 2006 .

[46]  M. McAleer,et al.  Asymmetry and Long Memory in Volatility Modeling , 2010 .

[47]  Jean-David Fermanian,et al.  Financial Valuation and Risk Management Working Paper No . 157 Some Statistical Pitfalls in Copula Modeling for Financial Applications , 2004 .

[48]  Xiaohong Chen,et al.  Estimation of Copula-Based Semiparametric Time Series Models , 2006 .