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Modelling the FRTB’s Default Risk Charge with a factor copula setup

Wisse, T.C. (2018) Modelling the FRTB’s Default Risk Charge with a factor copula setup.

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Abstract:In this research we develop a factor copula model to calculate the capital charges for default risk (DRC) under the regulations on the Fundamental Review of the Trading Book by the Basel Committee on Banking Supervision. The main model requirement for the DRC is the use of two systematic risk factors. To determine which copula to use in the model, we calibrate three copula approaches (Gaussian, Student-t and Clayton) to historical default data. Calibration of the copulas is done through the setup according to Vašíček's Large Homogeneous Pool. All three copula calibrations indicate a good fit to historical default data in a one systematic factor setup. The Gaussian and Student-t copula allow for direct use of two multiple factors for default modelling, where for the Clayton copula a nested copula approach needed. To calculate the DRC, we construct a long S\&P 500 portfolio and calculate the charge through the standardised approach (SA) and our internal models approach (IMA). The DRC model is constructed through regression analysis of standardised company returns against the Country and Sector returns. For model robustness, cluster analysis is performed through machine learning (regression tree). The DRC model is built using a Gaussian factor copula, and later enriched with the Student-t copula for more tail dependence. The Gaussian setup IMA charge of the highly diversified long portfolio is closely related to the SA charge. For multidirectional portfolios the DRC SA calculation proves to be very conservative compared to the developed model.
Item Type:Essay (Master)
KPMG, Amstelveen, Netherlands
Faculty:BMS: Behavioural, Management and Social Sciences
Subject:31 mathematics, 83 economics
Programme:Industrial Engineering and Management MSc (60029)
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