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Operational Risk Modeling:Theory and Practice
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Modellering av Operationell Risk: Teori och Praktik (Swedish)
Abstract [en]

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.

Abstract [sv]

Detta examensarbete studerarLoss Distribution Approach för modellering av Operationell Risk enligt Basel IIfrån en praktiskt och generell synvinkel. Inledande analys stödjer användandetav Peaks-over-Threshold-metoden för modellering av distributionen för varjeenskild förlust i en given cell.    Vi implementerar och diskuterar en metod för viktning avförlustdata med urvalsfel. Metoden bygger på en modell där varjeförlusthändelse registreras om och endast om förlusten överstiger ett utfallfrån en stokastisk tröskelvariabel. Metoden visas vara mycket användbar, menmedför flertalet utmaningar som kräver resonemang av kvalitativ art.   De mest kända estimatorerna av både extremvärdeströskeln ochparametrarna i den Generaliserade Pareto Distributionen granskas och studerasutifrån ett teoretiskt perspektiv. Vi introducerar även en GPD-estimator somanvänder ett momentbaserat estimat av formparametern, medan skalparameternskattas genom att anpassa en specifik hög kvantil till empirisk data. Allaestimatorer appliceras sedan på tillgänglig data och utvärderas med avseende påbåde robusthet och anpassning till data.    Vi går vidare igenom en analytisk approximation av det regulativakapitalestimatet för varje cell och applicerar denna på vår modell.Approximationens giltighet utvärderas sedan genom jämförelser med motsvarandeMonte-Carlo-estimat. Detta leder oss även in på studier av hur konvergensen avMonte-Carlo-estimaten beror på hur tungsvansad distributionen för varje enskildförlust är.   En standardmodell för korrelation emellan celler diskuteras, ochexplicita uttryck som begränsar modellens egentliga korrelation mellanaggregerade förlustdistributioner presentas. Dessa begränsningar skattas sedannumeriskt med hjälp av data.  

Place, publisher, year, edition, pages
2013. , 70 p.
Series
Trita-MAT-E, 2013:58
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-137370OAI: oai:DiVA.org:kth-137370DiVA: diva2:680983
External cooperation
Nordea
Subject / course
Mathematical Statistics
Educational program
Master of Science in Engineering -Engineering Physics
Supervisors
Examiners
Available from: 2013-12-19 Created: 2013-12-13 Last updated: 2013-12-19Bibliographically approved

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