The impact of estimation frequency on Value at Risk (VaR) and Expected Shortfall (ES) forecasts: an empirical study on conditional extreme value models

Coyne, Alice Elizabeth

The impact of estimation frequency on Value at Risk (VaR) and Expected Shortfall (ES) forecasts: an empirical study on conditional extreme value models

Master Thesis

2020

Abstract

This study investigates extreme market events which occur in the tails of a distribution. The extreme events occur with a very low probability, but with significant consequences, which is what makes them of interest. In this study 20 years of data from both the S&P 500 and the JSE All Share index have been used. An extreme value approach has been taken to quantify the risks associated with extreme market events. To achieve this a two phased process is used to calculated the Value at Risk and Expected Shortfall. The first phase involved running the daily returns through the GARCH model, and then extracting the residuals. The second phase involves using the Block Maxima Method, or Peaks over Threshold method to fit the residuals to the Generalized Extreme Value Distribution or the Generalized Pareto Distribution. Finally, the impact of estimation frequency is considered for each of the models. In conclusion, taking an extreme value approach to provide a statistically sound method to calculate risk, even when the parameters of the model are updated less frequently, this is preferable to simpler models where the parameter estimates are updated daily.

Keywords

Mathematical Statistics

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