Nov
6

## VaR and Expected shortfall under Generalized Student t

Value at risk (VaR) is the expected maximum loss an asset or a portfolio can incur over a target horizon within a given confidence level; Expected Shortfall (ES), also called Conditional tail expectation (CTE), is the expectation of the losses bigger (that is, worse) than VaR over a target horizon within a given confidence level. There are several methods in calculating VaR, including Historical simulation, Monte Carlo simulation, and parametric method, dozens of underlying distributions are ready for choice when using Monte Carlo simulation and Parametric method, among which Gaussian distribution is, undoubtedly the most popular one, t-distribution is also widely used due to its ability to capture fat-tail.

A sample Matlab code to construct the Generalized Student t over a given support then compute quantiles and numerical expected shortfall is http://www.hec.unil.ch/matlabcodes/Econometrics/TestGTdens.m.

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A sample Matlab code to construct the Generalized Student t over a given support then compute quantiles and numerical expected shortfall is http://www.hec.unil.ch/matlabcodes/Econometrics/TestGTdens.m.

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