Introduction In the last few years the quantitative modelling of credit risk has received a lot of attention within the financial industry. Several models have been released to the public, notably CreditRisk+, CreditMetrics, Credit Portfolio View [CR97, CM97, CP98]. Although different approaches to credit risk are used, studies have shown that the models yield similar results if the parameters ...

We consider the risk of a portfolio comprising loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in performance measures such as the probability that the portfolio incurs large losses over a fixed time horizon, and the expected excess loss given that large losses are incurred during this horizon. Contrary to the normal copula that is ...

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. Portfolio credit risk measurement is greatly affected by data...

One of the most significant developments in international credit markets in recent years has been the trade in Collateralized Debt Obligations (CDO), which has enabled financial institutions to repackage the credit risk of an asset portfolio into tranches to be transferred to investors. The present paper evaluates the credit risk of such a portfolio and the related tranches by applying two prom...

We review different methods for simulating credit migrations in a nonparametric and discrete or continuous-time Markov chain framework. We suggest the application of a factor model approach in combination with the use of copulas for the joint dynamics of credit rating changes. While there are several applications of copulas in credit risk for modeling joint defaults, it lacks of the same intere...

Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Valueat-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the contex...

Credit risk represents by far the biggest risk in the activities of a traditional bank. In particular, during recession periods financial institutions loose enormous amounts as a consequence of bad loans and default events. Traditionally the risk arising from a loan contract could not be transferred and remained in the books of the lending institution until maturity. This has changed completely...

We derive a formula for a Fourier transform of a counting process that describes the arrival of unpredictable events, and we show how this transform facilitates an analytical treatment of a range of valuation, hedging and risk management problems that arise in single name and portfolio credit risk. Example applications include reduced form pricing of credit sensitive securities referenced on si...

Simulation is widely used to estimate losses due to default and other credit events in financial portfolios. The challenge in doing this efficiently results from (i) rareevent aspects of large losses and (ii) complex dependence between defaults of multiple obligors. We discuss importance sampling techniques to address this problem in two portfolio credit risk models developed in the financial i...