We investigate a multi-factor extension of the asymptotic single risk factor (ASRF) model that underlies the capital charges of the quot;Basel II Accordquot;. In this extended model, it is still possible to derive closed-form solutions for the risk contributions to Value-at-Risk and Expected...

An evergreen debate in Finance concerns the rules for making portfolio hedge decisions. A traditional tool proposed in the literature is the well-known standard deviation based Sharpe Ratio, which has been recently generalized in order to involve also other popular risk measures p, such as VaR...

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...

Assessing the discriminative power of rating systems is an important question to banks and to regulators. In this article we analyze the Cumulative Accuracy Profile (CAP) and the Receiver Operating Characteristic (ROC) which are both commonly used in practice. We give a test-theoretic...

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...