The objective of this article is to prepare a time-inhomogeneous intensity model for valuing cash-flow CDOs, which explicitly incorporates the credit rating of the firms in the collateral portfolio as the indicator of the likelihood of default. Our model can prove very useful for the pricing, structuring, rating and risk management of CDO notes, whenever the legal structure of the transaction, ...

This paper presents a semi-analytical valuation method for basket credit derivatives in a flexible intensity-based model. Default intensities are modeled as correlated affine jump-diffusions. An empirical application documents that the model fits market prices of benchmark basket credit derivatives reasonably well, consistent with the observed correlation skew. Hence, I argue, contrary to comme...

In 2005 the Internal Ratings Based (IRB) approach of ‘Basel II’ was enhanced by a ‘treatment of double default effects’ to account for credit risk mitigation techniques such as ordinary guarantees or credit derivatives. This paper reveals several severe problems of this approach and presents a new method to account for double default effects. This new asset drop technique can be applied within ...

We show that the saddle-point approximation method to quantify the impact of undiversified idiosyncratic risk in a credit portfolio is inappropriate in the presence of double default effects. Specifically, we prove that there does not exist an equivalent formula to the granularity adjustment, that accounts for guarantees, in case of the extended single-factor CreditRisk model. Moreover, in case...

The 2008 crisis highlighted the importance of using stress tests in banking practice. The role of these stress tests is to identify and precisely estimate the effect of possible future changes in economic conditions on the capital adequacy and profitability of banks. This paper seeks to show a possible methodology to calculate the stressed point-in-time PD parameter. The presented approach cont...

The occurrence of defaults within a bond portfolio is modeled as a simple hidden Markov process. The hidden variable represents the risk state, which is assumed to be common to all bonds within one particular sector and region. After describing the model and recalling the basic properties of hidden Markov chains, we show how to apply the model to a simulated sequence of default events. Finally,...

Based onUKdata formajor retail credit cards,we build severalmodels of Loss GivenDefault based on account level data, including Tobit, a decision tree model, a Beta and fractional logit transformation. We find that Ordinary Least Squares models with macroeconomic variables perform best for forecasting Loss Given Default at the account and portfolio levels on independent hold-out data sets. The i...

In this note, we show on a stylised example how one can hedge Basket Credit Derivatives using a related family of liquid hedging products. Using simple Non-Arbitrage arguments and results from stochastic calculus, we prove that one can build a self-financing portfolio written on Credit Default Swaps which replicates the payoff of a general Credit Derivative.

We give a unified mathematical framework for reduced-form models for portfolio credit risk and identify properties which lead to positive dependence of default times. Dependence in the default hazard rates is modeled by common macroeconomic factors as well as by inter-obligor links. It is shown that popular models produce positive dependence between defaults in terms of association. Implication...

Default is a rare event, even in segments in the midrange of a bank’s portfolio. Inference about default rates is essential for risk management and for compliance with the requirements of Basel II. Most commercial loans are in the middle-risk categories and are to unrated companies. Expert information is crucial in inference about defaults. A Bayesian approach is proposed and illustrated using ...