Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES...

Intuitively, the default risk of a single borrower is higher when her or his assets and debt are denominated in different currencies. Additionally, the default dependence of borrowers with assets and debt in different currencies should be stronger than in the one-currency case. By combining...

Approximate Incremental Value-at-Risk formulae provide an easy-to-use preliminary guideline for risk allocation. Both the cases of risk adding and risk pooling are examined and beta-based formulae achieved. Results highlight how much the conditions for adding new risky positions are stronger...

By mid 2004, the Basel Committee on Banking Supervision (BCBS) is epected to launch its final recommendations on minimum capital requirements in the banking industry. Although there is the intention to arrive at capital charges which concur with economic intuition, the risk weight formulas...

The intention with this paper is to provide all the estimation concepts and techniques that are needed to implement a two-phases approach to the parametric estimation of probability of default (PD) curves. In the first phase of this approach, a raw PD curve is estimated based on parameters that...

Credit Suisse First Boston (CSFB) launched in 1997 the model CreditRisk+ which aims at calculating the loss distribution of a credit portfolio on the basis of a methodology from actuarial mathematics. Knowing the loss distribution, it is possible to determine quantile-based values-at-risk (VaRs)...

The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which...

PD curve calibration refers to the transformation of a set of rating grade level probabilities of default (PDs) to another average PD level that is determined by a change of the underlying portfolio-wide PD. This paper presents a framework that allows to explore a variety of calibration...

As a consequence of the dependence experienced in loan portfolios, the standard binomial test which is based on the assumption of independence does not appear appropriate for validating probabilities of default (PDs). The model underlying the new rules for minimum capital requirements (Basle II)...

This paper elaborates on the validation requirements for rating systems and probabilities of default (PDs) which were introduced with the New Capital Standards (Basel II). We start in Section 2 with some introductory remarks on the topics and approaches that will be discussed later on. Then we...