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Could Dynamic Variance-Covariance Settings and Jump Diffusion Techniques Enhance the Accuracy of Risk Measurement Models? A Reality Test. Li, Ming-Yuan Leon. Motivations. The importance of VaR (Value at Risk) The limitations of VaR Stress and scenario testing Improve the measurement of VaR.
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Could Dynamic Variance-Covariance Settings and Jump Diffusion Techniques Enhance the Accuracy of Risk Measurement Models? A Reality Test Li, Ming-Yuan Leon
Motivations • The importance of VaR (Value at Risk) • The limitations of VaR • Stress and scenario testing • Improve the measurement of VaR
Motivations • Three methods that are in common use to calculate VaR • (1) Parametric VaR • (2) Historical Simulation • (3) Monte Carlo Simulation • Relative strengths and weakness • VaR contribution (VaRC)
Motivations • Limitations of the parametric VaR • Stable variances and correlations • Poor description of extreme tail events • Solutions • Time-varying variances and covariance • A jump diffusion system • EVT (extreme value theory)
Literature review • Billio and Pelizzon (2000) & Li, et al. (2004) • Regime switching models to estimate VaR • Limitations of them: • Li (2004): univariate system • Billio and Pelizzon (2000) : a simple setting on variances
Literature review • Unlike them • Bivariate system • Not only state-varying technique but also time-varying process on the variances • Meaningful volatility-correlation relationship • Stable periods versus crisis periods
Model Specifications • The linear model with constant variance and covariance
Model Specifications • The MVGARCH model with time-varying variance and covariance
Model Specifications • The DCC proposed by Engle (2002):
Model Specifications • The jump diffusion model with regime-switching variance and covariance 1 X ARCH (r) g2 X ARCH (r)
Model Specifications Volatility-correlation relationship
Data • Daily index returns for the Canada, UK and US equity markets, as compiled by Morgan Stanley Capital International (MSCI) • The two portfolios addressed by this study are (1) Canada-US and (2) UK-US • The data cover the period from January 1st, 1990 through May 7th, 2007, and include 4,526 observations • All the stock prices are stated in dollar terms
Rolling estimation process • In the VaR back-testing, the final 2,500 daily observations of the sample are omitted from the initial sample • Ten back testing periods with the 250 daily observations for each period
Rolling estimation process • At time t, 2,026 (equal to 4,526 minus 2,500) historical data are incorporated into the estimation of the model parameters • Based on these variance and correlation estimates, the VaR estimates are then constructed • Two-step procedure in MVSWARCH model
Conclusions • During the stable period • The linear-based model and the three advanced VaR models behave similarly • During the crisis period • The linear-based model yields poorer results • The two MVGARCH and the MVSWARCH models do enhance the precision of VaR estimates in crisis periods
Three caveats • In crisis periods, the of exceptions obtained with the three advanced models is still higher than four, the upper bound for the “Green” zone • The improvement of the accuracy of VaR measurement obtained with the two dynamic correlation settings in comparison with the CCC-MVGARCH is less promising • A system with more than two dimensions