Value-at-Risk and Expected Shortfall estimation under conditional Extreme Value Theory framework : An empirical study in Nordic stock markets in 2005–2015

Abstract

The purpose of this research is to determine whether the currently used financial risk estimation methods for Value-at-Risk and Expected Shortfall are sufficient to measure financial risks and to conclude if it is beneficial to incorporate sophisticated risk estimation methods to gauge the nature of market risk adequately. Especially, the purpose of this thesis is to compare Extreme Value Theory based 99% VaR and 97.5% ES models to traditional risk models, as there is an ongoing discussion on whether the Basel Committee should replace the existing 99% VaR framework with 97.5% ES. To test whether more sophisticated tail risk estimation methods would result in more robust risk estimates, an EVT-GPD model was constructed for both VaR and ES, which models the tail of the loss distribution under the EVT framework and accounts for the conditional mean and variance by a GPD-GARCH method. To test the relative performance of the EVT-GPD model, AR(1)-GARCH(1,1) reference models were constructed with normal, skew normal, student t and skew student t innovation distributions. The risk models were compared by VaR and ES backtests and scoring function means. This research was conducted on Nordic stock market data consisting of OMXS, OMXH, OMXC and OMXI total return indices. The risk models were backtested during a full sample accounting for 2870 daily observations, as well as in a stresstesting period during the financial crisis accounting for 266 observations of the most violate market turbulence.

This research provides evidence that it is inevitable to incorporate non-normal risk estimation methods to obtain robust estimates of market risk and its build-up during both normal and extreme market circumstances. It was found that the risk models based on normal and skew normal distribution underestimate risk to a great extent even at lower quantiles and that the underestimation worsens at higher quantiles. The results also indicate that the EVT-GPD method is consistent as there is less variation in backtest acceptance at every tested quantile compared to the reference models for both VaR and ES. This research provides evidence that there is not notable difference in 99% VaR estimates between the EVT-GPD model and student models in the full sample, but the EVT-GPD model provides better estimates during the financial crisis, which implies that the EVT-GPD model seem to react quicker to prompt changes in markets. Moreover, the results suggest that the EVT-GPD method was doubtlessly the best model to estimate the 97.5% ES in terms of both the overall model acceptance and the scoring function based model ranking.

As the scoring function based method is new, an extensive amount of research is required to universalize the results and discover alternative risk estimation models that provide sound risk estimates in tranquil and volatile market circumstances.