Simulation of default events in a CDX and estimation of the spread

The portfolio generating the iTraxx EUR index is modeled by coupled Markov chains. Each of the industries of the portfolio evolves according to its own Markov transition matrix. Using a variant of the method of moments, the model parameters are estimated from a data set of Standard and Poor's. Swap spreads are evaluated by Monte-Carlo simulations. Along with an actuarially fair spread, at least squares spread is considered.

Hyperspectral unmixing based on mixtures of Dirichlet components

This paper introduces a new unsupervised hyperspectral unmixing method conceived to linear but highly mixed hyperspectral data sets, in which the simplex of minimum volume, usually estimated by the purely geometrically based algorithms, is far way from the true simplex associated with the endmembers. The proposed method, an extension of our previous studies, resorts to the statistical framework. The abundance fraction prior is a mixture of Dirichlet densities, thus automatically enforcing the constraints on the abundance fractions imposed by the acquisition process, namely, nonnegativity and sum-to-one. A cyclic minimization algorithm is developed where the following are observed: 1) The number of Dirichlet modes is inferred based on the minimum description length principle; 2) a generalized expectation maximization algorithm is derived to infer the model parameters; and 3) a sequence of augmented Lagrangian-based optimizations is used to compute the signatures of the endmembers. Experiments on simulated and real data are presented to show the effectiveness of the proposed algorithm in unmixing problems beyond the reach of the geometrically based state-of-the-art competitors.