Proxying credit curves via Wasserstein distances.

Credit risk plays a key role in financial modeling, and financial institutions are required to incorporate it in their pricing, as well as in capital requirement calculations. A common manner to extract credit worthiness information for existing and potential counterparties is based on the Credit Default Swap (CDS) market. Nonetheless, not all counterparties of a financial institution have (liquid) CDSs traded in the market.

Factor analysis models via I-divergence optimization.

Given a positive definite covariance matrix [Formula: see text] of dimension n, we approximate it with a covariance of the form [Formula: see text], where H has a prescribed number [Formula: see text] of columns and [Formula: see text] is diagonal. The quality of the approximation is gauged by the I-divergence between the zero mean normal laws with covariances [Formula: see text] and [Formula: see text], respectively. To determine a pair (H, D) that minimizes the I-divergence we construct, by lifting the minimization into a larger space, an iterative alternating minimization algorithm (AML) à la Csiszár-Tusnády.