Evaluating the performance of the Generalized Hyperbolic skew Student t-distribution in modeling risk via simulation studies

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Abstract The exponential-polynomial tail of the generalized hyperbolic skew Student-t distribution allows it to handle volatility asymmetry, heavy-semi heavy tails, and substantial skewness, thus the distribution has been found to be superiority in modelling volatility and extreme tail risk in comparison to competing distributions. However, because there are no known empirical tests to clearly differentiate between the tails of the empirical distribution of returns, one is likely to wrongly identify the generalized hyperbolic skew Student t-distribution as the true distribution. Under such circumstances, should one be worried about the accuracy of the forecasts? This is the question the study seeks to answer to provide insights to practitioners and researchers. In this regard, simulated returns are generated via GARCH framework under different distributional data generating assumptions and are then used to forecast volatility and tail risk to assess the performance of the different distributional assumptions. Observations from the results suggest that under a mis-specified distributional assumption for the true data generating process, the generalized hyperbolic skew Student-t distribution do not trade off forecast accuracies in for volatility and extreme tail risk forecasts but the same cannot be said about value-at-risk when the extreme returns occur below the quantile of interest. It is therefore recommended that when volatility and extreme tail risk forecasting is the objective of interest, and the tails of the returns are more Gaussian-like and exhibit substantial skewness, one should not be worried about the accuracy of the forecast when the generalized hyperbolic skew Student-t distribution is wrongly identified as the true distribution of the data generating process.

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