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Sensitivity analysis of volatility - a new tool for risk management

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Author Info
Simone Manganelli () (European Central Bank, Kaiserstrasse 29, Postfach 16 03 19, 60066 Frankfurt am Main, Germany.)
Vladimiro Ceci () (Tradinglab Banca S.p.A., Corso Italia 3, 20122 Milano, Italy.)
Walter Vecchiato () (IntesaBCI, Risk Management Department, Via Clerici 4, 20121 Milano, Italy.)

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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.

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Publisher Info
Paper provided by European Central Bank in its series Working Paper Series with number 194.

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Length: 38 pages
Date of creation: Nov 2002
Date of revision:
Handle: RePEc:ecb:ecbwps:20020194

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Related research
Keywords: Risk management; sensitivity analysis; dynamic correlations; GARCH.;

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 116-31, February. [Downloadable!] (restricted)
  2. Christian Gourieroux & J. P. Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Econometric Society World Congress 2000 Contributed Papers 0162, Econometric Society. [Downloadable!]
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  3. Robert F. Engle, 2000. "Dynamic Conditional Correlation - A Simple Class of Multivariate GARCH Models," University of California at San Diego, Economics Working Paper Series 2000-09, Department of Economics, UC San Diego. [Downloadable!]
  4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February. [Downloadable!]
    Other versions:
  5. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics. [Downloadable!]
    Other versions:
  6. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Kenneth D. West & Hali J. Edison & Dongchul Cho, 1992. "A Utility Based Comparison of Some Models of Exchange Rate Volatility," NBER Technical Working Papers 0128, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  9. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  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, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Panayiotis Diamandis & Georgios Kouretas & Leonidas Zarangas, 2006. "Asset allocation in the Athens Stock Exchange: A variance sensitivity analysis," Working Papers 0602, University of Crete, Department of Economics. [Downloadable!]
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