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Li, Ming-Yuan Leon

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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Li, Ming-Yuan Leon

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  1. Could Dynamic Variance-Covariance Settings and Jump Diffusion Techniques Enhance the Accuracy of Risk Measurement Models? A Reality Test Li, Ming-Yuan Leon

  2. Motivations • The importance of VaR (Value at Risk) • The limitations of VaR • Stress and scenario testing • Improve the measurement of VaR

  3. 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)

  4. 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)

  5. 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

  6. 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

  7. Model Specifications • The linear model with constant variance and covariance

  8. Model Specifications

  9. Model Specifications

  10. Model Specifications • The MVGARCH model with time-varying variance and covariance

  11. Model Specifications

  12. Model Specifications

  13. Model Specifications • The DCC proposed by Engle (2002):

  14. Model Specifications • The jump diffusion model with regime-switching variance and covariance 1 X ARCH (r) g2 X ARCH (r)

  15. Model Specifications Volatility-correlation relationship

  16. Model Specifications

  17. Back-testing of VaR Results

  18. Back-testing of VaR Results

  19. 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

  20. 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

  21. 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

  22. Parameter estimates

  23. Parameter estimates

  24. Parameter estimates

  25. Parameter estimates

  26. Parameter estimates

  27. Testing VaR results

  28. Testing VaR results

  29. Testing VaR results

  30. Testing VaR results

  31. Testing VaR results

  32. 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

  33. 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

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