Quantifying credit portfolio losses under multi-factor models

ABSTRACT

In this work, we investigate the challenging problem of estimating credit risk measures of portfolios with exposure concentration under the multi-factor Gaussian and multi-factor t-copula models. It is well-known that Monte Carlo (MC) methods are highly demanding from the computational point of view in the aforementioned situations. We present efficient and robust numerical techniques based on the Haar wavelets theory for recovering the cumulative distribution function of the loss variable from its characteristic function. To the best of our knowledge, this is the first time that multi-factor t-copula models are considered outside the MC framework. The analysis of the approximation error and the results obtained in the numerical experiments section show a reliable and useful machinery for credit risk capital measurement purposes in line with Pillar II of the Basel Accords.

KEYWORDS:

• Credit risk
• Value-at-Risk
• expected shortfall
• multi-factor models
• Gaussian copula
• t-copula
• Fourier transform inversion
• Haar wavelets

2010 AMS SUBJECT CLASSIFICATIONS:

• 91G60
• 62P05
• 60E10
• 65T60

JEL CODES:

• G32
• C63

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Note that we use as the definition for the characteristic function the Fourier transform of the density function.

2 The programs are coded in MATLAB and run in a laptop with processor 2 GHz intel core i5 and memory 8 GB 1867 MHz LPDDR3.

Additional information

Funding

The research leading to these results has received funding from La Caixa Foundation. G. C.-P. acknowledges AGAUR-Generalitat de Catalunya for funding under its doctoral scholarship programme. G. C.-P. and L. O.-G. acknowledge the Spanish Ministry of Economy and Competitiveness for funding under grants [ECO2016-76203-C2-2] and [MTM2016-76420-P] (MINECO/FEDER, UE).