| Summary: | Value-at-risk quantifies the amount of capital needed to handle future losses on investments at a given confidence level. The Covid-19 pandemic greatly increased market volatility, which motivates us to investigate value-at-risk models during this time period. We account for stylized facts of asset returns by modelling the returns with a GARCH(1,1) process under suitable distributional assumptions for the standardized noise such as Student's $t$, normal inverse Gaussian, and Meixner. We also include the historically dominant value-at-risk model that combines the powers of extreme value theory and GARCH(1,1) processes. Firstly we assess the performance both pre-Covid-19 and intra-Covid-19 by traditional backtesting and also by a studying the loss, and secondly we investigate the model risk in order to quantify the uncertainty associated with model selection. While all models struggled intra-Covid-19, the models based on normal inverse Gaussian noise, Meixner noise, and extreme value theory performed the best overall. The model that assumes Gaussian noise was only competitive at less extreme quantiles, while the model that assumes Student's $t$ noise struggled at less extreme quantiles due to being too liberal. Despite the models' struggle intra-Covid-19, the model risk remained at a similar level throughout market calm and market stress.
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