The performance of Value-at-Risk models on the OBX index

Abstract

The measuring of risk has become one of the main fields in finance during the last two decades. Value-at-Risk (VaR) has become one of the most important risk measures and is widely used for numerous applications. This thesis compares different approaches to VaR based on traditional methods such as Historical Simulation, Moving Average and Exponentially Weighted Moving Average as well as advanced approaches based on GARCH models. Comparison is done on the OBX index return data, which is the main benchmark index on the Oslo Stock Exchange. The performance of the different VaR models is evaluated with out of sample backtests over two periods of changing market conditions. The first period is the crisis period with high volatility and market uncertainty that covers the financial crisis in 2008. The second period is the post crisis period after the financial crisis that has more normal market conditions. Our findings are that traditional VaR methods do not capture the risk of the OBX index. The models tend to underestimate the risk when the market goes through a crisis and generally perform poorly. Several of the VaR models based on GARCH dynamics perform quite well and overall the best model is the skew Student-t GARCH(1,1) which is not rejected in any backtest and therefore captures the risk in both the crisis period and the post crisis period. The model also outperforms sophisticated GARCH models that are able to capture asymmetries in volatility and power effects. The choice of error distribution for the GARCH models is also found to be very important. Changing the normal error distribution to the skew Student-t distribution significantly improves the forecasting performance of the GARCH models.