The computation of value at risk under time varying volatility models

Abstract

Over the past decades, there are many financial institutions which suffered acute losses or collapsed because of poor risk management. In response to these events, practitioners, researchers and bankers have to develop more reliable and powerful tools in risk management. One of the most widely adopted concepts in market risk management is Value at Risk (VaR). VaR is a statistical measure of the risk that estimates the maximum loss that may be experienced on a portfolio with a given level of confidence over a given time horizon. The objective of this study is to check whether there exists a simple and a reliable model to compute VaR or not. Parametric and nonparametric approaches are presented. In addition, study of different types of time varying volatility models are also performed. For the univariate case, the study compare three different time varying volatility models, i.e the ARCH(1) model, the EWMA model and the SV model. For the multivariate study, we looked at the behaviour of the EWMA model, the O-EWMA model and the O-GARCH(1,1) model. These models are estimated on Chicago Fed Midwest Manufacturing Index (CFMMI) monthly indices. Finally, backtesting are performed to validate the VaR models.