The probability density function for survivals, that is for transitions without hitting the barrier, for a collection of particles driven by correlated Brownian motions is analyzed. The analysis is known to lead one to a study of the spectrum of the Laplacian on domains on the sphere in higher...

The probability density function for survivals, that is for transitions without hitting a barrier, for a collection of particles driven by correlated Brownian motions is analyzed. The analysis is known to lead to a study of the spectrum of the Laplacian on domains on the sphere in higher...

The May 2005 crisis and the recent credit crisis have indicated to us that any realistic model of default dependency needs to account for at least two risk factors, firm-specific and catastrophic. Unfortunately, the popular Gaussian copula model has no identifiable support to either of these. In...

This article presents a model of default dependency based on Levy subordinator. It is a tractable dynamical model, computationally structured similar to the one-factor Gaussian copula model, providing easy calibration to individual hazard rate curves and efficient pricing with Fast Fourier...

A class of mean reverting positive stochastic processes driven by alpha-stable distributions, referred to here as alpha-root processes in analogy to the square root process (Cox-Ingersoll-Ross process), is a subclass of affine processes, in particular continuous state branching processes with...

The article presents a model of default dependency based on Levy subordinator. It is a tractable one-factor model with an architecture similar to that of the standard Gaussian copula model, providing easy calibration to individual hazard rate curves and efficient pricing with Fast Fourier...

Subordinators are Levy processes with non-decreasing sample paths. They are natural processes to model default dependency. They help ensure that the loss process is non-decreasing leading to a promising class of dynamic models. The simplest subordinator is the Levy subordinator, a maximally...

The jump distribution for the default intensities in a reduced form framework is modeled and calibrated to provide reasonable fits to CDX.NA.IG and iTraxx Europe CDOs, to 5, 7 and 10 year maturities simultaneously. Calibration is carried out using an efficient Monte Carlo simulation algorithm...

The jump distribution for the default intensities in a reduced form framework is modeled and calibrated to provide reasonable fits to CDX.NA.IG and iTraxx Europe CDOs, to 5, 7 and 10 year maturities simultaneously. Calibration is carried out using an efficient Monte Carlo simulation algorithm...

Delayed, hence non-simultaneous, dependent defaults are discussed in a reduced form model. The model is a generalization of a multi-factor model based on simultaneous defaults to incorporate delayed defaults. It provides a natural smoothening of discontinuities in the joint probability densities...