Skip to main content
Top
Published in:
Cover of the book

2017 | OriginalPaper | Chapter

1. VaR in High Dimensional Systems-A Conditional Correlation Approach

Authors : H. Herwartz, B. Pedrinha, F. H. C. Raters

Published in: Applied Quantitative Finance

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In empirical finance, multivariate volatility models are widely used to capture both volatility clustering and contemporaneous correlation of asset return vectors. In higher dimensional systems, parametric specifications often become intractable for empirical analysis owing to large parameter spaces. On the contrary, feasible specifications impose strong restrictions that may not be met by financial data as, for instance, constant conditional correlation (CCC). Recently, dynamic conditional correlation (DCC) models have been introduced as a means to solve the trade off between model feasibility and flexibility. Here, we employ alternatively the CCC and the DCC modeling framework to evaluate the Value-at-Risk associated with portfolios comprising major U.S. stocks. In addition, we compare their performances with corresponding results obtained from modeling portfolio returns directly via univariate volatility models.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
go back to reference Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking and Finance, 26, 1487–1503.CrossRef Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking and Finance, 26, 1487–1503.CrossRef
go back to reference Alexander, C. O. (1998). Volatility and correlation: Measurement, models and applications. In Alexander (Ed.), Risk management and analysis: Measuring and modelling financial risk (pp. 125–171). New York: Wiley. Alexander, C. O. (1998). Volatility and correlation: Measurement, models and applications. In Alexander (Ed.), Risk management and analysis: Measuring and modelling financial risk (pp. 125–171). New York: Wiley.
go back to reference Alexander, C. O. (2001). Orthogonal GARCH. In Alexander (Ed.), Mastering risk (Vol. II, pp. 21–38). Upper Saddle River: Prentice Hall. Alexander, C. O. (2001). Orthogonal GARCH. In Alexander (Ed.), Mastering risk (Vol. II, pp. 21–38). Upper Saddle River: Prentice Hall.
go back to reference Baba, Y., Engle, R. F., Kraft, D. F., & Kroner, K. F. (1990). Multivariate Simultaneous Generalized ARCH, mimeo, Department of Economics. San Diego: University of California. Baba, Y., Engle, R. F., Kraft, D. F., & Kroner, K. F. (1990). Multivariate Simultaneous Generalized ARCH, mimeo, Department of Economics. San Diego: University of California.
go back to reference Bauwens, L., Laurent, S., & Rombouts, J. V. K. (2006). Multivariate GARCH models: A survey. Journal of Applied Econometrics, 21, 79–109.MathSciNetCrossRef Bauwens, L., Laurent, S., & Rombouts, J. V. K. (2006). Multivariate GARCH models: A survey. Journal of Applied Econometrics, 21, 79–109.MathSciNetCrossRef
go back to reference Black, F. (1976). Studies of stock price volatility changes. In Proceedings of the American Statistical Association, Business and Economic Statistics Section (pp. 177–191). Black, F. (1976). Studies of stock price volatility changes. In Proceedings of the American Statistical Association, Business and Economic Statistics Section (pp. 177–191).
go back to reference Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. The Review of Economics and Statistics, 72, 498–505.CrossRef Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. The Review of Economics and Statistics, 72, 498–505.CrossRef
go back to reference Bollerslev, T., & Wooldridge, J. M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews, 11, 143–172.MathSciNetCrossRefMATH Bollerslev, T., & Wooldridge, J. M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews, 11, 143–172.MathSciNetCrossRefMATH
go back to reference Bollerslev, T., Engle, R. F., & Nelson, D. B. (1994). ARCH models. In R. F. Engle & D. L. McFadden (Eds.), Handbook of econometrics (Vol. 4, pp. 2959–3038). Amsterdam: Elsevier. Bollerslev, T., Engle, R. F., & Nelson, D. B. (1994). ARCH models. In R. F. Engle & D. L. McFadden (Eds.), Handbook of econometrics (Vol. 4, pp. 2959–3038). Amsterdam: Elsevier.
go back to reference Bollerslev, T., Engle, R. F., & Wooldridge, J. M. (1988). A capital asset pricing model with time-varying covariances. Journal of Political Economy, 96, 116–131.CrossRef Bollerslev, T., Engle, R. F., & Wooldridge, J. M. (1988). A capital asset pricing model with time-varying covariances. Journal of Political Economy, 96, 116–131.CrossRef
go back to reference Campbell, S. D. (2006). A review of backtesting and backtesting procedures. The Journal of Risk, 9, 1–17.CrossRef Campbell, S. D. (2006). A review of backtesting and backtesting procedures. The Journal of Risk, 9, 1–17.CrossRef
go back to reference Cappiello, L., Engle, R. F., & Sheppard, K. (2006). Asymmetric dynamics in the correlations of global equity and bond returns. Journal of Financial Econometrics, 4, 537–572.CrossRef Cappiello, L., Engle, R. F., & Sheppard, K. (2006). Asymmetric dynamics in the correlations of global equity and bond returns. Journal of Financial Econometrics, 4, 537–572.CrossRef
go back to reference Cecchetti, S. G., Cumby, R. E., & Figlewski, S. (1988). Estimation of the optimal futures hedge. The Review of Economics and Statistics, 70, 623–630.CrossRef Cecchetti, S. G., Cumby, R. E., & Figlewski, S. (1988). Estimation of the optimal futures hedge. The Review of Economics and Statistics, 70, 623–630.CrossRef
go back to reference Chib, S., Nardari, F., & Shephard, N. (2006). Analysis of high dimensional multivariate stochastic volatility models. Journal of Econometrics, 134, 341–371.MathSciNetCrossRefMATH Chib, S., Nardari, F., & Shephard, N. (2006). Analysis of high dimensional multivariate stochastic volatility models. Journal of Econometrics, 134, 341–371.MathSciNetCrossRefMATH
go back to reference Christoffersen, P., Hahn, J., & Inoue, A. (2001). Testing and comparing value-at-risk measures. Journal of Empirical Finance, 8, 325–342.CrossRef Christoffersen, P., Hahn, J., & Inoue, A. (2001). Testing and comparing value-at-risk measures. Journal of Empirical Finance, 8, 325–342.CrossRef
go back to reference Comte, F., & Lieberman, O. (2003). Asymptotic theory for multivariate GARCH processes. Journal of Multivariate Analysis, 84, 61–84.MathSciNetCrossRefMATH Comte, F., & Lieberman, O. (2003). Asymptotic theory for multivariate GARCH processes. Journal of Multivariate Analysis, 84, 61–84.MathSciNetCrossRefMATH
go back to reference Ding, Z. & Engle, R. F. (2001). Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing, mimeo, NYU. Ding, Z. & Engle, R. F. (2001). Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing, mimeo, NYU.
go back to reference Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.MathSciNetCrossRefMATH Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.MathSciNetCrossRefMATH
go back to reference Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics, 20, 339–350.MathSciNetCrossRef Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics, 20, 339–350.MathSciNetCrossRef
go back to reference Engle, R. F., & Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH. Econometric Theory, 11, 122–150.MathSciNetCrossRef Engle, R. F., & Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH. Econometric Theory, 11, 122–150.MathSciNetCrossRef
go back to reference Engle, R. F., & Mezrich, J. (1996). GARCH for groups. Risk, 9, 36–40. Engle, R. F., & Mezrich, J. (1996). GARCH for groups. Risk, 9, 36–40.
go back to reference Engle, R. F. & Sheppard, K. (2001). Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH, mimeo, National Bureau of Economic Research. Engle, R. F. & Sheppard, K. (2001). Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH, mimeo, National Bureau of Economic Research.
go back to reference Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics, 22, 367–381.MathSciNetCrossRef Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics, 22, 367–381.MathSciNetCrossRef
go back to reference Engle, R. F., Ito, T., & Lin, W. L. (1990a). Meteor showers or heat waves? heteroskedastic intra-daily volatility in the foreign exchange market. Econometrica, 58, 525–542. Engle, R. F., Ito, T., & Lin, W. L. (1990a). Meteor showers or heat waves? heteroskedastic intra-daily volatility in the foreign exchange market. Econometrica, 58, 525–542.
go back to reference Engle, R. F., Ng, V. M., & Rothschild, M. (1990b). Asset pricing with a factor-ARCH covariance structure: Empirical estimates for treasury bills. Journal of Econometrics, 45, 213–237. Engle, R. F., Ng, V. M., & Rothschild, M. (1990b). Asset pricing with a factor-ARCH covariance structure: Empirical estimates for treasury bills. Journal of Econometrics, 45, 213–237.
go back to reference Ghalanos, A. (2015). rmgarch: Multivariate GARCH models, R package version 1.3-0. Ghalanos, A. (2015). rmgarch: Multivariate GARCH models, R package version 1.3-0.
go back to reference Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779–1801.CrossRef Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779–1801.CrossRef
go back to reference Hafner, C. M., & Herwartz, H. (1998). Structural analysis of portfolio risk using beta impulse response functions. Statistica Neerlandica, 52, 336–355.CrossRefMATH Hafner, C. M., & Herwartz, H. (1998). Structural analysis of portfolio risk using beta impulse response functions. Statistica Neerlandica, 52, 336–355.CrossRefMATH
go back to reference Hafner, C. M. & Franses, P. H. (2003). A Generalized Dynamic Conditional Correlation Model for Many Assets, Econometric Institute Report 18, Erasmus University Rotterdam. Hafner, C. M. & Franses, P. H. (2003). A Generalized Dynamic Conditional Correlation Model for Many Assets, Econometric Institute Report 18, Erasmus University Rotterdam.
go back to reference Hafner, C. M., & Herwartz, H. (2008). Analytical quasi maximum likelihood inference in multivariate volatility models. Metrika, 67, 219–239.MathSciNetCrossRefMATH Hafner, C. M., & Herwartz, H. (2008). Analytical quasi maximum likelihood inference in multivariate volatility models. Metrika, 67, 219–239.MathSciNetCrossRefMATH
go back to reference Hafner, C. M., van Dijk, D., & Franses, P. H. (2006). Semi-parametric modelling of correlation dynamics. In Fomby & Hill (Eds.), Advances in econometrics part A (Vol. 20, pp. 59–103). New York: Elsevier Science. Hafner, C. M., van Dijk, D., & Franses, P. H. (2006). Semi-parametric modelling of correlation dynamics. In Fomby & Hill (Eds.), Advances in econometrics part A (Vol. 20, pp. 59–103). New York: Elsevier Science.
go back to reference Hamao, Y., Masulis, R. W., & Ng, V. K. (1990). Correlations in price changes and volatility across international stock markets. Review of Financial Studies, 3, 281–307.CrossRef Hamao, Y., Masulis, R. W., & Ng, V. K. (1990). Correlations in price changes and volatility across international stock markets. Review of Financial Studies, 3, 281–307.CrossRef
go back to reference Jeantheau, T. (1998). Strong consistency of estimators for multivariate ARCH models. Econometric Theory, 14, 70–86.MathSciNetCrossRef Jeantheau, T. (1998). Strong consistency of estimators for multivariate ARCH models. Econometric Theory, 14, 70–86.MathSciNetCrossRef
go back to reference Jorion, P. (2007). Value at risk: The new benchmark for managing financial risk (2nd ed.). New York: McGraw Hill. Jorion, P. (2007). Value at risk: The new benchmark for managing financial risk (2nd ed.). New York: McGraw Hill.
go back to reference Lee, S. W., & Hansen, B. E. (1994). Asymptotic theory for the GARCH(1,1) quasi-maximum likelihood estimator. Econometric Theory, 10, 29–52.MathSciNetCrossRef Lee, S. W., & Hansen, B. E. (1994). Asymptotic theory for the GARCH(1,1) quasi-maximum likelihood estimator. Econometric Theory, 10, 29–52.MathSciNetCrossRef
go back to reference Lee, T. H., & Long, X. (2009). Copula-based multivariate GARCH model with uncorrelated dependent errors. Journal of Econometrics, 150, 207–218.MathSciNetCrossRefMATH Lee, T. H., & Long, X. (2009). Copula-based multivariate GARCH model with uncorrelated dependent errors. Journal of Econometrics, 150, 207–218.MathSciNetCrossRefMATH
go back to reference Ling, S., & McAleer, M. (2003). Asymptotic theory for a vector ARMA-GARCH model. Econometric Theory, 19, 280–310.MathSciNet Ling, S., & McAleer, M. (2003). Asymptotic theory for a vector ARMA-GARCH model. Econometric Theory, 19, 280–310.MathSciNet
go back to reference Lütkepohl, H. (1996). Handbook of matrices. Chichester: Wiley.MATH Lütkepohl, H. (1996). Handbook of matrices. Chichester: Wiley.MATH
go back to reference Lumsdaine, R. L. (1996). Consistency and asymptotic normality of the quasi-maximum likelihood estimator in IGARCH(1,1) and covariance stationary GARCH(1,1) models. Econometrica, 64, 575–596.MathSciNetCrossRefMATH Lumsdaine, R. L. (1996). Consistency and asymptotic normality of the quasi-maximum likelihood estimator in IGARCH(1,1) and covariance stationary GARCH(1,1) models. Econometrica, 64, 575–596.MathSciNetCrossRefMATH
go back to reference Nakatani, T. (2014). ccgarch: An R Package for Modelling Multivariate GARCH Models with Conditional Correlations. R package version 0.2.3. Nakatani, T. (2014). ccgarch: An R Package for Modelling Multivariate GARCH Models with Conditional Correlations. R package version 0.2.3.
go back to reference Newey, W. K., & McFadden, D. (1994). Large sample estimation and hypothesis testing. In Engle & McFadden (Eds.), Handbook of econometrics (Vol. 4, pp. 2111–2245). Amsterdam: Elsevier. Newey, W. K., & McFadden, D. (1994). Large sample estimation and hypothesis testing. In Engle & McFadden (Eds.), Handbook of econometrics (Vol. 4, pp. 2111–2245). Amsterdam: Elsevier.
go back to reference Ruud, P. A. (2000). An introduction to classical econometric theory. Berkeley: University of California. Ruud, P. A. (2000). An introduction to classical econometric theory. Berkeley: University of California.
go back to reference Tse, Y. K. (2000). A test for constant correlations in a multivariate GARCH model. Journal of Econometrics, 98, 107–127.CrossRefMATH Tse, Y. K. (2000). A test for constant correlations in a multivariate GARCH model. Journal of Econometrics, 98, 107–127.CrossRefMATH
go back to reference Tse, Y. K., & Tsui, A. K. C. (2002). A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics, 20, 351–362.MathSciNetCrossRef Tse, Y. K., & Tsui, A. K. C. (2002). A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics, 20, 351–362.MathSciNetCrossRef
go back to reference Van der Weide, R. (2002). GO-GARCH: A multivariate generalized orthogonal GARCH model. Journal of Applied Econometrics, 17, 549–564.CrossRef Van der Weide, R. (2002). GO-GARCH: A multivariate generalized orthogonal GARCH model. Journal of Applied Econometrics, 17, 549–564.CrossRef
Metadata
Title
VaR in High Dimensional Systems-A Conditional Correlation Approach
Authors
H. Herwartz
B. Pedrinha
F. H. C. Raters
Copyright Year
2017
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-54486-0_1