Numerically stable computation of CreditRisk+

The CreditRisk+ model launched by CSFB in 1997 is widely used by practitioners in the banking sector as a simple means for the quantification of credit risk, primarily of the loan book. We present an alternative numerical recursion scheme for CreditRisk+, equivalent to an algorithm recently proposed by Giese, based on well-known expansions of the logarithm and the exponential of a power series. We show that it is advantageous to the Panjer recursion advocated in the original CreditRisk+ document, in that it is numerically stable. The crucial stability arguments are explained in detail. Furthermore, the computational complexity of the resulting algorithm is stated

Systemic Risk and Default Clustering for Large Financial Systems

As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and computational tools for the quantification of such phenomena. Limiting analysis such as law of large numbers and central limit theorems allow to approximate the distribution in large systems and study quantities such as the loss distribution in large portfolios. Large deviations analysis allow us to study the tail of the loss distribution and to identify pathways to default clustering. Sensitivity analysis allows to understand the most likely ways in which different effects, such as contagion and systematic risks, combine to lead to large default rates. Such results could give useful insights into how to optimally safeguard against such events.Comment: in Large Deviations and Asymptotic Methods in Finance, (Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer Proceedings in Mathematics and Statistics, Vol. 110 2015

Basel II and fostering the disclosure of banks\' internal credit ratings

ISSN:1566-7529ISSN:1741-620

An Analytical Approach for Systematic Risk Sensitivity of Structured Finance Products

The global financial crisis has shown that many financial institutions dealing with credit derivatives were exposed to severe unexpected losses. This indicates that systematic influences are decisively underestimated particularly with regard to structured products like securitized tranches of collateralized debt obligations. Our analytical study addresses these systematic effects: We provide a simple model which allows a closed-form comparison of both bonds and tranches with respect to their systematic risk. We demonstrate that the exposure to systematic risk of tranches may be many times higher than the exposure of bonds, even if both products share the same rating grade, e.g., an ‘AAA’ rating, measured by either default probability or expected loss. Particularly in economic downturns, default rates of tranches may be multiples of those of bonds. Our results help understand high default rates of tranches during the financial crisis and show that classical ratings are insufficient metrics for measuring risks of structured products

The credit risk + model with general sector correlations

Credit risk + , Compound gamma distribution, Value at risk, Risk contribution, Correlation, Portfolio loss distribution, Moment generating function,