KTH Matematik  

Matematisk Statistik

Tid: 18 december 2013 kl 11.15-12.00.

Seminarierummet 3721, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7.

Föredragshållare: Johan Wahlström

Titel: Operational Risk Modeling: Theory and Practice (Examensarbete - Master thesis)

Abstract This thesis studies the Loss Distribution Approach for modeling of Operational Risk under Basel II from a practical and general perspective. Initial analysis supports the use of the Peaks over Threshold method for modeling the severity distributions of individual cells. A method for weighting loss data subject to data capture bias is implemented and discussed. The idea of the method is that each loss event is registered if and only if it exceeds an outcome of a stochastic threshold. The method is shown to be very useful, but poses some challenges demanding the employment of qualitative reasoning. The most well known estimators of both the extreme value threshold and the parameters in the Generalized Pareto Distribution are reviewed and studied from a theoretical perspective. We also introduce a GPD estimator which uses the Method-of-Moments estimate of the shape parameter while estimating the scale parameter by fitting a specific high quantile to empirical data. All estimators are then applied to available data sets and evaluated with respect to robustness and data fit. We further review an analytical approximation of the regulatory capital for each cell and apply this to our model. The validity of the approximation is evaluated by using Monte Carlo estimates as a benchmark. This also leads us to study how the rate of convergence of the Monte Carlo estimates depends on the "heavy-tailedness" of the loss distribution. A standard model for correlation between cells is discussed and explicit expressions limiting the actual correlation between the aggregated loss distributions in the model are presented. These bounds are then numerically estimated from data.

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Sidansvarig: Filip Lindskog
Uppdaterad: 31/01-2013