Risikostyring i lyset af den finansielle krise: Udvidelser af de klassiske Value at Risk og Expected Shortfall modeller

Mads Lerche Iversen & Jørgen Larsen Laugesen

Student thesis: Master thesis

Abstract

The purpose of this thesis is to investigate various methods for estimation of market risk. Our investigation is based on a comparative study of two parametric -, a semi parametric - and a non-parametric model. The aim of the models is to consistently estimate the actual market risk through periods of financial distress. We use two well known risk measures, namely Value at Risk (VaR) and Expected Shortfall (ES) and provide results and key findings. Models are estimated and tested for ten selected stocks from the Danish OMXC20 index. At first we define a variance model. The recent year has shown a significant increase in market volatility due to the financial turmoil and has stressed the need for a valid variance model. We test various models to assess which of these provides the best fit. We find that the GARCH(1,2) model leads to the best test results and this is used throughout the thesis as the model for variance. The parametric models consist of a class of generalized hyperbolic (GH) distributions. These include the normal distribution as well as symmetric- and asymmetric distributions. Of several GH distribution families considered, the most successful is the skewed-t distribution (sometimes referred to as the skewed Student-t distribution). We compare VaR and ES estimates for the skewed-t and the normal distribution as the latter is the most commonly used in practice. Furthermore, we introduce a non-parametric - and a semi parametric model which are not restricted by the same distributional assumptions as the fully parametric models. The first model is the well known Historical Simulation (HS) approach which is commonly used in financial institutions. The second model is Filtered Historical Simulation (FHS) which originates from the HS approach, but incorporates a model for the variance. Both use historical simulation schemes. VaR and ES estimates are provided for both models and it is shown that the HS model overestimates risk in periods of low volatility and vice versa. Furthermore, the backtesting procedure rejects the HS model whereas it accepts the FHS model. The general conclusion is that a market risk measure must essentially incorporate a model for the variance as an indicator for changes in market volatility. In addition, results indicate that the introduction of more complex distributions (GH) leads to a more consistent measure of risk.

EducationsMSc in Mathematics , (Graduate Programme) Final Thesis
LanguageDanish
Publication date2009
Number of pages136