Estimating value at risk using extreme value theory : is the two dimensional inhomogeneous Poisson model better than the others
1University of Oulu, Oulu Business School, Department of Finance, Finance
|Online Access:||PDF Full Text (PDF, 1.5 MB)|
|Persistent link:|| http://urn.fi/URN:NBN:fi:oulu-201510152084
|Publish Date:|| 2015-10-19
|Thesis type:||Master's thesis
This research presents an application of extreme value theory to estimate the value at risk of a market position particularly of the OMX Hex Index. There are many approaches to computing value at risk alongside the extreme value method. One fundamental problem the manager of risk face is “what is the optimal choice of value at risk estimator that will best predict the risk?” This implies that choosing an approach to best predict value at risk is challenging. This study proposed a method of estimating value at risk using the two-dimensional inhomogeneous Poisson model. An extreme value theory method that is based on the Peak Over Threshold (POT). The method takes into consideration time varying parameters through some explanatory variables. The study also shows how well theoretical model fit real financial data. The data used is the daily log return of the OMX Hex Index from the period 1990 to 2014.
From the data we show empirically that the OMX Hex Index obeys a Fréchet distribution. The explanatory variables for the study are GARCH volatilities, annual trend and quarter dummies. The explanatory variables are all available at time t-1. With the help of the fitted models we adopt the two-dimensional inhomogeneous Poisson model approach to estimating value at risk over the two-dimensional homogeneous Poisson model and other classical or traditional methods, and find that this better predict value at risk estimates.
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