Backtesting Bootstrap Value-at-Risk and Expected Shortfall estimates in GARCH models (Master Dissertation)

data_sample.R: Data wrangling and analysis
methods.R: Risk estimation methods
backtests.R: Backtesting methods
implementation_backtesting.R: Implementation of risk estimation and backtesting methods

Abstract

This work focuses on the, to our best knowledge, first application and backtesting of the bootstrap methods in GARCH models of Pascual et al. (2006) and Chen et al. (2011) to the estimation of value-at-risk and expected shortfall, using data from the FTSE 100 index, as well as the comparison of their performance with the ones of the Filtered Historical Simulation and Historical Simulation. The accurate estimation of these risk measures is significantly relevant to the risk management decisions of financial institutions, as well as to fulfill the regulatory requirements, such as the ones imposed by the Basel II Accords. Previous existing methods have some limitations, such not including the uncertainty due to parameter estimation. In addition to the computational costs of the method developed by Chen et al. (2011) being 100 times lower than the one of Pascual et al. (2006), the former assumes a symmetric conditional return distribution, which, according to the empirical application developed in this work, seems to have a positive impact on the accuracy of the risk measures generated. Moreover, both methods seem to outperform the Historical Simulation and the Filtered Historical Simulation, as the former imposes unnecessary capital requirements to financial institutions, while the latter fails to predict extreme losses.