The paper proposes a new method to estimate correlation of account-level Basel II Loss Given Default (LGD). The correlation determines the probability distribution of portfolio level LGD in the context of a copula model which is used to stress the LGD parameter as well as to estimate the LGD discount rate and other parameters. Given historical LGD observations, the maximum likelihood method is applied to estimate the best correlation parameter. The method is applied and analyzed on a real large dataset of unsecured retail account-level LGDs and the corresponding monthly series of the average LGDs. The correlation estimate obtained is relatively close to the PD regulatory correlation. It is also tested for stability using the bootstrapping method and used in an efficient formula to estimate the ex ante one-year stressed LGD, i.e., one-year LGD quantiles on any reasonable probability level.

The Basel II regulatory formula (BCBS, 2006) aims to provide a sufficiently robust estimate of the unexpected losses on banking credit exposures that should be covered by the capital. The capital requirement (C) is set equal to the difference between the unexpected (UL) and expected credit loss (EL), calculated for each receivable as C = UL - EL = (UDR - PD) × LGD × EAD, where PD is the expected default rate, UDR = UDR(PD) a specific regulatory function estimating unexpected default rate from the PD parameter, LGD the expected percentage loss conditional upon default, and EAD the expected exposure of the receivable at default.

The regulatory approach (BCBS, 2006; and CRD, 2006) is very specific regarding the unexpected default rate applying the Vasicek (1987) formula that is generally considered to be sufficiently robust. On the other hand, the LGD parameter is specified very vaguely by the regulation to reflect downturn economic conditions, but may be also calculated just as a long-term default weighted average under relatively normal circumstances. This deficiency has been criticized by many practitioners and researchers (Altman et al., 2004).

The importance of stressing all the Basel II parameters is underlined by the 2007 economic crisis. The Committee on Banking Supervision has already issued several proposals, revisions and enhancement of the Basel II regulation reacting to the crisis. In order to strengthen banks' stress testing practices, as well as to improve supervision of those practices, in May 2009, the Committee published Principles for Sound Stress Testing Practices and Supervision. The regulatory package issued in July 2009 also covers risk management principles, securitized assets, market risk, and the trading activities.

Financial Risk Management Journal, Banking Supervision, Risk Management Principles, Market Risk, Bootstrapping Method, Parametric Beta Distribution, Extrapolation Techniques, Asymptotic Model, LGD Correlation Methodology, Extrapolation Methods, Basel II Regulation.