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Value–at–Risk Models

In: Handbook of Financial Time Series

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  • Peter Christoffersen

    (McGill University, Desautels Faculty of Management)

Abstract

In this chapter, we build first a univariate and then a multivariate filtered historical simulation (FHS) model for financial risk management. Both the univariate and multivariate methods simulate future returns from a model using historical return innovations. While the former relies on portfolio returns filtered by a dynamic variance model, the latter uses individual or base asset return innovations from dynamic variance and correlation models. The univariate model is suitable for passive risk management or risk measurement whereas the multivariate model is useful for active risk management such as optimal portfolio allocation. Both models are constructed in such a way as to capture the stylized facts in daily asset returns and to be simple to estimate. The FHS approach enables the risk manager to easily compute Value-at-Risk and other risk measures including Expected Shortfall for various investment horizons that are conditional on current market conditions. The chapter also lists various alternatives to the suggested FHS approach.

Suggested Citation

  • Peter Christoffersen, 2009. "Value–at–Risk Models," Springer Books, in: Thomas Mikosch & Jens-Peter Kreiß & Richard A. Davis & Torben Gustav Andersen (ed.), Handbook of Financial Time Series, chapter 33, pages 753-766, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-71297-8_33
    DOI: 10.1007/978-3-540-71297-8_33
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