What happens after a default: the conditional density approach

M ay 2 00 9 What happens after a default : the conditional density approach ∗

We present a general model for default time, making precise the role of the intensity process, and showing that this process allows for a knowledge of the conditional distribution of the default only “before the default”. This lack of information is crucial while working in a multi-default setting. In a single default case, the knowledge of the intensity process does not allow to compute the pr...

ON THE STATIONARY PROBABILITY DENSITY FUNCTION OF BILINEAR TIME SERIES MODELS: A NUMERICAL APPROACH

In this paper, we show that the Chapman-Kolmogorov formula could be used as a recursive formula for computing the m-step-ahead conditional density of a Markov bilinear model. The stationary marginal probability density function of the model may be approximated by the m-step-ahead conditional density for sufficiently large m.

Recall Activity: What Happens before and after Basal Cell Carcino-mas’ Surgery?

An Approach to Default Reasoning Based on a First-Order Conditional Logic

This paper presents an approach to default reasoning based on an extension to classical first-order logic. In this approach, first -order logic is augmented with a “variable conditional” operator for representing default statements. Truth in the resulting logic is based on a possible worlds semantics: the default statement C-P is true just when p is true in the least exceptional worlds in which...

Exact Fit of Simple Finite Mixture Models

How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed...