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Sensitivity analysis of volatility: a new tool for risk management

Author

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  • Ceci, Vladimiro
  • Manganelli, Simone
  • 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

  • Ceci, Vladimiro & Manganelli, Simone & Vecchiato, Walter, 2002. "Sensitivity analysis of volatility: a new tool for risk management," Working Paper Series 194, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:2002194
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    References listed on IDEAS

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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.

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    More about this item

    Keywords

    Dynamic Correlations; GARCH; risk management; Sensitivity Analysis;
    All these keywords.

    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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