This paper analyzes a family of multivariate point process models of correlated event timing whose arrival intensity is driven by an affine jump diffusion. The components of an affine point process are selfand cross-exciting, and facilitate the description of complex event dependence structures. Ordinary differential equations characterize the transform of an affine point process and the probab...

We consider a bottom-up Markovian copula model of portfolio credit risk where instantaneous contagion is possible in the form of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula set-up. In this sense this model solves the bottom...

In this paper we propose a new, information-based approach for modelling the dynamic evolution of a portfolio of credit risky securities. In our setup market prices of traded credit derivatives are given by the solution of a nonlinear filtering problem. The innovations approach to nonlinear filtering is used to solve this problem and to derive the dynamics of market prices. Moreover, the practi...

We model aggregate credit losses on large portfolios of financial positions contracted with firms subject to both cyclical default correlation and direct default contagion processes. Cyclical correlation is due to the dependence of firms on common economic factors. Contagion is associated with the local interaction of firms with their business partners. We provide an explicit normal approximati...

This paper develops approximations for the distribution of losses from default in a normal copula framework for credit risk. We put particular emphasis on approximating small probabilities of large losses, as these are the main requirement for calculation of value at risk and related risk measures. Our starting point is an approximation to the rate of decay of the tail of the loss distribution ...

The financial crisis of 2007 – 2009 began with a major failure in credit markets. The causes of this failure stretch far beyond inadequate mathematical modeling (see Donnelly and Embrechts [2010] and Brigo et al. [2009] for detailed discussions from a mathematical finance perspective). Nevertheless, it is clear that some of the more popular models of credit risk were shown to be flawed. Many of...

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 credit card portfolio management, predicting the cardholder’s spending behavior is a key to reduce the risk of bankruptcy. Given a set of attributes for major aspects of credit cardholders and predefined classes for spending behaviors, this paper proposes a classification model by using multiple criteria linear programming to discover behavior patterns of credit cardholders. It shows a gener...

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 ...