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 impact of default events on the loss distribution of a credit portfolio can be assessed by determining the loss distribution conditional on these events. While it is conceptually easy to estimate loss distributions conditional on default events by means of Monte Carlo simulation, it becomes...

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...

This paper presents analytical solutions to the problem of how to calculate sensible VaR (Value-at-Risk) and ES (Expected Shortfall) contributions in the CreditRisk+ methodology. Via the ES contributions, ES itself can be exactly computed in finitely many steps. The methods are illustrated by...