Honour Thesis: A Joint Value at Risk and Expected Shortfall Combination Framework and its Applications in the Cryptocurrency Market

Value at risk and expected shortfall are increasingly popular tail risk measures in the financial risk management field. Both academia and financial institutions are working to improve tail risk forecasts in order to meet the requirements of the Basel Capital Accord; it states that one purpose of risk management and measuring risk accuracy is, since extreme movements cannot always be avoided, financial institutions can prepare for these extreme returns by capital allocation, and putting aside the appropriate amount of capital so as to avoid default in times of extreme price or index movements. Forecast combination has drawn much attention, as a combined forecast can outperform the individual forecasts under certain conditions. We propose two methodology, one is a semiparametric combination framework that can jointly produce combined value at risk and expected shortfall forecasts, another one is a parametric regression framework named as Quantile-ES regression that can produce combined expected shortfall forecasts. The favourability of the semiparametric combination framework has been presented via an empirical study - application in cryptocurrency markets with high-frequency data where the necessity of risk management application increases as the cryptocurrency market becomes more popular and mature. Additionally, the general framework of the parametric Quantile-ES regression has been presented via a simulation study, whereas it still need to be improved in the future. The contributions of this work include but are not limited to the enabling of the combination of expected shortfall forecasts and the application of risk management procedures in the cryptocurrency market with high-frequency data.