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Sensitivity analysis of volatility: a new tool for risk management

Author

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  • Manganelli, Simone
  • Ceci, Vladimiro
  • Vecchiato, Walter

Abstract

The extension of GARCH models to the multivariate setting has been fraught with difficulties. In this paper, we suggest to work with univariate portfolio GARCH models. We show how the multivariate dimension of the portfolio allocation problem may be recovered from the univariate approach. The main tool we use is the "variance sensitivity analysis", which measures the change in the portfolio variance as a consequence of an infinitesimal change in the portfolio allocation. We derive the sensitivity of the univariate portfolio GARCH variance to the portfolio weights, by analytically computing the derivatives of the estimated GARCH variance with respect to these weights. We suggest a new and simple method to estimate full variance-covariance matrices of portfolio assets. An application to real data portfolios shows how to implement our methodology and compares its performance against that of selected popular alternatives. JEL Classification: C32, C53, G15

Suggested Citation

  • Manganelli, Simone & Ceci, Vladimiro & Vecchiato, Walter, 2002. "Sensitivity analysis of volatility: a new tool for risk management," Working Paper Series 0194, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:20020194
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    File URL: http://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp194.pdf
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    References listed on IDEAS

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    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    4. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    5. West, Kenneth D. & Edison, Hali J. & Cho, Dongchul, 1993. "A utility-based comparison of some models of exchange rate volatility," Journal of International Economics, Elsevier, vol. 35(1-2), pages 23-45, August.
    6. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
    7. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    8. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    9. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    10. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    11. Engle, Robert F, 2000. "Dynamic Conditional Correlation - A Simple Class of Multivariate GARCH Models," University of California at San Diego, Economics Working Paper Series qt56j4143f, Department of Economics, UC San Diego.
    12. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Chrétien, Stéphane & Ortega, Juan-Pablo, 2014. "Multivariate GARCH estimation via a Bregman-proximal trust-region method," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 210-236.
    2. Panayiotis F. Diamandis & Anastassios A. Drakos & Georgios P. Kouretas & Leonidas P. Zarangas, 2012. "Asset allocation in the Athens stock exchange: a variance sensitivity analysis," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 17(2), pages 167-181, April.
    3. St'ephane Chr'etien & Juan-Pablo Ortega, 2011. "Multivariate GARCH estimation via a Bregman-proximal trust-region method," Papers 1101.5475, arXiv.org.

    More about this item

    Keywords

    Dynamic Correlations; GARCH; risk management; Sensitivity Analysis;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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