The purpose of this paper is to discuss two important extensions to the well‐known value‐at‐risk (VaR) methodology, namely extreme value theory (EVT) and expected shortfall (ES). Both of these extensions address the weaknesses of VaR, in particular the methodology's tendency to systematically underestimate risk of extreme market events.
The theory of VaR and the two extensions are reviewed and the methodology is evaluated in light of the Basel II regulatory framework that calls for the use of VaR by financial institutions.
The paper clarifies the use of VaR and its extensions to make practitioners more aware of the pitfalls and how to address them. It is recommended that the two extended measures of extreme event risk (i.e. EVT and ES) be included into every risk manager's information pool.
A compact review of these approaches and their regulatory connection has not previously been compiled. This review is of particular value to risk managers and policy markers given the turbulent market conditions of the past year.
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