The Promise and the Peril of Parametric Value-at-Risk (VaR) Analysis

Central Bank Journal of Law and Finance, vol. 2, no. 1, pp. 1-42 (2015)

42 Pages Posted: 8 Jun 2015 Last revised: 22 Aug 2016

James Ming Chen

Michigan State University - College of Law

Date Written: June 8, 2015

Abstract

Leptokurtosis, or the risk lurking in “fat tails,” poses the deepest epistemic threat to economic forecasting. Parametric value-at-risk (VaR) models are extremely vulnerable to kurtosis in excess of the levels associated with a normal, Gaussian distribution. This article provides step-by-step guidance on the use of Student’s t-distribution to enhance the statistical robustness of VaR forecasts. For degrees of freedom greater than 4, Student’s t-distribution can emulate any level of kurtosis exceeding that of a Gaussian distribution. Because VaR is elicitable from historical data, observed levels of excess kurtosis can inform the proper use of Student’s t-distribution to measure value-at-risk. In addition, the calculation of parametric VaR according to the number of degrees of freedom implied by historical levels of excess kurtosis leads directly to the corresponding value of expected shortfall. Conducted in this fashion, parametric VaR not only exploits the elicitability of that quantile-based measure, but also informs the computation of expected shortfall as a theoretically coherent risk measure.

Suggested Citation

Chen, James Ming, The Promise and the Peril of Parametric Value-at-Risk (VaR) Analysis (June 8, 2015). Central Bank Journal of Law and Finance, vol. 2, no. 1, pp. 1-42 (2015). Available at SSRN: https://ssrn.com/abstract=2615664 or http://dx.doi.org/10.2139/ssrn.2615664

James Ming Chen (Contact Author)

Michigan State University - College of Law ( email )

318 Law College Building
East Lansing, MI 48824-1300
United States

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