| Summary: | This dissertation aims to examine the performance of different risk measures with three international indices: S&P 500, FTSE250 and HSI. The study compared four distribution candidates used in modelling the Value at Risk (VaR) and expected shortfall (ES) estimates with 95% significant level aiming to analyse the quality of them in producing 1-day ahead forecasts as well as consider the more accurate prediction when the index returns have their volatility conditioning with GARCH model. The VaR and ES forecasts were computed from unconditional and conditional models applied to four distribution candidates which were the Historical Simulation, the Gaussian model, the Student-t distribution as well as Generalised Pareto distribution using extreme value theory.
For its framework for analysis, the study made use of modelling the risk estimates to observe an over- or underestimate model with a formal statistic procedure, backtesting. Three different VaR backtests (the violation ratio; Kupiec, 1995; Christoffersen, 1998) and an ES backtest (McNeil-Frey, 2000) were employed for an assessment. The results from three markets were producing similar results suggesting that the model with an assumption of an extreme event was not proper for the tranquil period and the unconditional model with normality assumption was preferred in the VaR forecast. The Historical Simulation provided a satisfying number of VaR violations but failed a test on time dependency. Although the ES was more conservative than the VaR, more alternatives on the conditional models can be selected for accurate 1-day ES forecasts. Incorporating GARCH in distribution modelling improved ES forecasting performance.
Keywords: Value-at-Risk, Expected Shortfall, Backtesting, Unconditional models, Conditional models
|
|---|