Estimating Value at Risk (VaR) and Expected Shortfall Using Normal Weighted Inverse Gaussian Distributions


The VaR for Normal Weighted Inverse Gaussian (NWIG) distributions is calculated in this paper. Measures of potential risk for losses in the financial markets include Value at Risk (VaR) and Expected Shortfall (ES). When addressing VaR and ES, the Normal Inverse Gaussian (NIG) distribution, a particular instance of the Generalized Hyperbolic Distribution (GHD), is frequently used in literature. However, there are other unique applications for the GHD known as Normal Inverse Gaussian Related Distributions that can be exploited. Value at Risk would be replaced with Expected Shortfall, as advocated by the Basel Committee [1], but it was decided that backtesting would continue to be done using VaR even if capital would be based on Expected Shortfall. Therefore, the two risk measurements that have been most widely used and beneficial in financial management are still those two. The Expectation Maximization (EM) technique has been used to obtain the Maximum Likelihood (ML) estimations of the suggested models for the financial data from Range Resource Corporation (RRC). We used the Kupiec likelihood ratio to backtest VaR. (LR). The Kolmogorov-Smirnov and Anderson-Darling tests have been used in the goodness of fit test. The Akaike Information Creterion (AIC), Bayesian Information Creterion (BIC), and Log-likelihood have all been applied to the model selection process. The results clearly show that for computing VaR and ES, the NWIG distributions are suitable replacements for NIG.

Author(s) Details:

Calvin B. Maina,
Department of Mathematics and Actuarial Science, Kisii University, Kisii, Kenya.

Patrick G. O. Weke,
School of Mathematics, University of Nairobi, Nairobi, Kenya.

Carolyne A. Ogutu,
School of Mathematics, University of Nairobi, Nairobi, Kenya.

Joseph A. M. Ottieno,
School of Mathematics, University of Nairobi, Nairobi, Kenya.

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Keywords: Risk measures, backtesting, weighted distribution, normal mixture, EM-algorithm

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