Geostatistical modeling of dependent credit spreads: Estimation of large covariance matrices and imputation of missing data

Abstract

Abstract We explore how the joint modeling of financial assets, especially dependent credit spreads, can utilize methodologies from geostatistical modeling. The considered approach is essentially based on modeling data as realizations of a (Gaussian) random field. This allows for a parsimonious representation of the dependence structure by means of a covariance function taken to be a function of the distance between observations. A key benefit of this ansatz is the possibility to include new data points, i.e. to consider new companies in existing financial applications. Consequently, geostatistical modeling has appealing benefits in the context of covariance matrix estimation and missing data imputation. We thoroughly discuss the necessary adjustments when applying geostatistical methods to the high-dimensional framework that entails the modeling of financial data, instead of the 2D/3D coordinate space encountered in original applications of the method. We illustrate the two use cases of covariance matrix estimation and missing data imputation on a data set of CDS spreads of constituents of the iTraxx universe, and sketch how the presented techniques could be exploited for market risk modeling.