We present an extension to the Gaussian copula model with jumps. We mix normal distributions which have negative means and small weights with the standard normal distribution in the Gaussian copula model to generate jumps in the default probability distribution for each underlying credit. The means and weights of the new normal distributions are used to control the size and intensity of the jum...

The nature and intensity of punishment following contractual default varies greatly across economies. For instance, in the residential mortgage context, some US states limit the liability of the borrower to the home, while other states grant the lender much broader recourse. Intuitively, we would expect these differences to matter for default behavior at the micro-economic level and for equilib...

In this article we estimate default intensities within the continuous time Jarrow/Turnbull (1995) model from daily observations of German bank bond prices, based on the default-free term structure estimated from the Svensson (1994) model provided by the Deutsche Bundesbank. Cross-sectional and time-series estimations are performed. We show that pricing errors from the term structure estimation ...

This paper looks at both the prepayment risks of housing mortgage loan credit default swaps (LCDS) as well as the fuzziness and hesitation of investors as regards prepayments by borrowers. It further discusses the first default pricing of a basket of LCDS in a fuzzy environment by using stochastic analysis and triangular intuition-based fuzzy set theory. Through the 'fuzzification' of the sensi...

We consider the problem of computing some basic quantities such as defaultable bond prices and survival probabilities in a credit risk model according to the intensity based approach. We let the default intensities depend on an external factor process that we assume is not observable. We use stochastic filtering to successively update its distribution on the basis of the observed default histor...

We review the pricing of synthetic CDO tranches from the point of view of factor models. Thanks to the factor framework, we can handle a wide range of well-know pricing models. This includes pricing approaches based on copulas, but also structural, multivariate Poisson and affine intensity models. Factor models have become increasingly popular since there are associated with efficient semi-anal...

The aim of these notes is to provide a relatively concise but still self-contained overview of mathematical notions and results which underpin the valuation of defaultable claims. Though the default risk modelling was extensively studied in numerous recent papers, it seems nonetheless that some of these papers lack a sound theoretical background. Our goal is to furnish results which cover both ...

In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We essentially show how to use structural models with a calibration capability that is typical of the much more tractable credit-spread based intensity models. W...

In single-obligor default risk modelling, using a background filtration in conjunction with a suitable embedding hypothesis (generally known as H-hypothesis or immersion property) has proven a very successful tool to separate the actual default event from the model for the default arrival intensity. In this paper we analyze the conditions under which this approach can be extended to the situati...

We propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allow...