Mixture models play an important role in the modeling of portfolio losses. In these models the risk of default of individual obligors (indexed by i ∈ {1, . . . ,m}) depends on an underlying set of common economic factors, denoted Ψ. Given these factors, the losses due to default li of individual obligors are assumed to be stochastically independent. Dependence between different obligors stems o...

A change of shares of credits portfolio is described by Markov chain with discrete time. A credit state is determined on as an accessory to some group of credits depending on presence of indebtedness and its terms. We use a model with discrete time and fix the system state through identical time intervals once a month. It is obvious that the matrix of transitive probabilities is known incomplet...

We consider mathematical models for portfolio credit risk. We analyze the mathematical structure and in particular the modelling of dependence between default events in these models and propose extensions of standard industry models. We study the model risk related to the choice of model structure and input parameters. Finally we develop and test several approaches to model calibration in credi...

Even in the simple Vasicek one-factor credit portfolio model, the exact contributions to credit value-at-risk cannot be calculated without Monte-Carlo simulation. As this may require a lot of computational time, there is a need for approximate analytical formulae. In this note, we develop formulae according to two different approaches: the granularity adjustment approach initiated by M. Gordy a...

Traditionally, the literature on financial intermediation and credit channels, especially credit crunches, emphasized the relation between banks and entrepreneurs requiring credit, neglecting the funding of banks. With this paper, we want to be much more precise in this respect and study the impact of funding on credit. Indeed, regulation that has become world wide with the Basle Accord puts li...

We compare the performance of various hedging strategies for index collateralized debt obligation (CDO) tranches across a variety of models and hedging methods during the recent credit crisis. Our empirical analysis shows evidence for market incompleteness: a large proportion of risk in the CDO tranches appears to be unhedgeable. We also show that, unlike what is commonly assumed, dynamic model...

2 Continuous-Time Markov Chains 3 2.1 Time-homogeneous chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Time-inhomogeneous chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Embedded Discrete-Time Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Conditional Expectations . . . . . . . . . . . . . . . . . . ...

Even in the simple Vasicek credit portfolio model, the exact contributions to credit value-at-risk cannot be calculated without Monte-Carlo simulation. As this may require a lot of computational time, there is a need for approximative analytical formulae. In this note, we develop formulae according to two different approaches: the granularity adjustment approach initiated by M. Gordy and T. Wil...

The Credit Risk+ model is one of the industry standards for estimating the credit default risk for a portfolio of credit loans. The natural parameterization of this model requires the default probability to be apportioned using a number of (non-negative) factor loadings. However, in practice only default correlations are often available but not the factor loadings. In this paper we investigate ...