Multiday expected shortfall under generalized t distributions: evidence from global stock market
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Multiday expected shortfall under generalized t distributions: evidence from global stock market Robina Iqbal1 · Ghulam Sorwar1 · Rose Baker1 · Taufiq Choudhry2
© The Author(s) 2020
Abstract We apply seven alternative t-distributions to estimate the market risk measures Value at Risk (VaR) and its extension Expected Shortfall (ES). Of these seven, the twin t-distribution (TT) of Baker and Jackson (in Twin t distribution, University of Salford Manchester. https://arxiv.org/abs/1408.3237, 2014) and generalized asymmetric distribution (GAT) of Baker (in A new asymmetric generalization of the t-distribution, University of Salford Manchester. https://arxiv.org/abs/1606.05203, 2016) are applied for the first time to estimate market risk. We analytically estimate VaR and ES over 1-day horizon and extend this to multi-day horizon using Monte Carlo simulation. We find that taken together TT and GAT distributions provide the best back-testing results across individual confidence levels and horizons for majority of scenarios. Moreover, we find that with the lengthening of time horizon, TT and GATmodels performs well, such that at the 10-day horizon, GATprovides the best back-testing results for all of the five indices and the TT model provides the second best results, irrespective period of study and confidence level. Keywords Generalize t distribution · Asymmetric t distribution · Expected shortfall · EGARCH models · Multi-days ahead expected shortfall JEL Classification C13 · C15 · C51 · C52 · C53 · C58 · G17
* Ghulam Sorwar [email protected] Robina Iqbal [email protected] Rose Baker [email protected] Taufiq Choudhry [email protected] 1
Salford Business School, University of Salford, Manchester M5 4WT, UK
2
Southampton Business School, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK
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1 Introduction From its very beginnings in the 1980s Value-at-Risk (VaR) as a measure of market risk has received widespread acceptance both amongst industry and regulators on account of its ease of calculation and intuitive interpretation. In its most basic form, VaR provides the worst possible loss at a given confidence level over a specific horizon. The main drawback of VaR, other than, that it is a single number is that there is no one accepted way of calculating it. It is possible that the use of different models will lead to different VaRs and that this could be very costly to financial institutions. In that, if VaR is over estimated, then the institution is tying of capital which it could use elsewhere for a higher return; or if it under estimates, then the firm is severely exposed to market down turns as it has not set aside correct amount of capital. The financial crisis of 2007–2008 has illustrated the drawbacks in stark terms of the VaR methodology and this has resulted in debate amongst academics, regulators and market practitioners. As part of this debate, the related measure to VaR, the expected shortfall (ES) is now giv
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