A rolling analysis on the prediction of value at risk with multivariate GARCH and copula

Abstract

Risk management has been a crucial part of the daily operations of the financial industry over the past two decades. Value at Risk (VaR), a quantitative measure introduced by JP Morgan in 1995, is the most popular and simplest quantitative measure of risk. VaR has been widely applied to the risk evaluation over all types of financial activities, including portfolio management and asset allocation. This paper uses the implementations of multivariate GARCH models and copula methods to illustrate the performance of a one-day-ahead VaR prediction modeling process for high-dimensional portfolios. Many factors, such as the interaction among included assets, are included in the modeling process. Additionally, empirical data analyses and backtesting results are demonstrated through a rolling analysis, which help capture the instability of parameter estimates. We find that our way of modeling is relatively robust and flexible.