Economic Capital Models : Methods for fitting loss distributions

University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

Abstract: The thesis provides a well-researched classical approach to fit and predict the losses (extreme) for Lloyds Bank’s Dutch mortgage portfolio, their defaulted Dutch mortgage portfolio, and their German personal and car loan portfolio. This is a crucial piece for quantification of the economic loss, required for effective credit risk management by the Bank. For starters, the distribution of losses needs to be defined in order to determine the amount of losses that a bank can possibly experience in an event that corresponds to a specific confidence level. To get to that point, the data needs to be approximated with either one or more distributions, this thesis covers the single distribution approach and the mixture model approach that uses two distributions to solve the approximation of the data. Our work concludes that the optimal distribution for the regular Dutch mortgage portfolio losses include a Beta-Beta mixture and a Lognormal-Gamma mixture. Where the Lognormal-Gamma mixture has utilized a threshold approach that splits the data into two separate data sets and then fits the data separately before combining them with a weight function. While, for the second Dutch mortgage portfolio at the specific snapshots, the Beta and the Generalized Pareto outperformed the rest. Furthermore, for the German personal and car loan portfolio, the Generalized Pareto also performed the best. This is a crucial step for calculating the necessary economic capital that Lloyds Banking Group plans to do in the near future.

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