Transformational Approach to Analytical Value-at-Risk for near Normal Distributions

Puneet Prakash, Vikas Sangwan and Kewal Singh
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Puneet Prakash: Department of Finance and General Business, Missouri State University, 901 S. National Avenue, Springfield, MO 65897, USA
Vikas Sangwan: Department of Industrial and Management Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Kewal Singh: Department of Industrial and Management Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

JRFM, 2021, vol. 14, issue 2, 1-19

Abstract: In this paper, we extend the parametric approach of VaR estimation that is based upon the application of two transforms, one for handling skewness and other for kurtosis. These transformations restore normality to data when applied in succession. The transforms are well defined and offer an alternative to VaR models based on the variance–covariance approach. We demonstrate the application of the technique using three pairs of uncorrelated but negatively skewed and fat-tailed stock return distributions, one pair each from recent periods in US and international market, and one from the stressed period of US economic history. Furthermore, we extend the analysis to economic domain by calculating expected shortfalls and risk capital under different estimation methods. For the sake of completion, we compare the estimation results of normal and transformation methods to non-parametric historical simulation.

Keywords: value-at-risk; normal distribution; manly transform; John and Draper transform; GARCH (1, 1); back-testing; risk capital; expected shortfall (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2021
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