could dynamic variance-covariance settings and jump diffusion techniques enhance the accuracy of...
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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 tim
e-varying process on the variances– Meaningful volatility-correlation relationship– Stable periods versus crisis periods
Model Specifications
• The linear model with constant variance and covariance
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Model Specifications
• The MVGARCH model with time-varying variance and covariance
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Model Specifications
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Model Specifications
• The DCC proposed by Engle (2002):
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Model Specifications
• The jump diffusion model with regime-switching variance and covariance
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Model Specifications
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Volatility-correlation relationship
Model Specifications
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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 advanc
ed VaR models behave similarly
• During the crisis period – The linear-based model yields poorer results – The two MVGARCH and the MVSWARCH mo
dels 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