Climbing Down from the Top: Single Name Dynamics in Credit Top Down Models

In the top-down approach to multi-name credit modeling, calculation of singe name sensitivities appears possible, at least in principle, within the so-called random thinning (RT) procedure which dissects the portfolio risk into individual contributions. We make an attempt to construct a practical RT framework that enables efficient calculation of single name sensitivities in a top-down framework, and can be extended to valuation and risk management of bespoke tranches. Furthermore, we propose a dynamic extension of the RT method that enables modeling of both idiosyncratic and default-contingent individual spread dynamics within a Monte Carlo setting in a way that preserves the portfolio “top”-level dynamics. This results in a model that is not only calibrated to tranche and single name spreads, but can also be tuned to approximately match given levels of spread volatilities and correlations of names in the portfolio. We would like to thank Andrew Abrahams, Anil Bangia, Tom Bielecki, Rama Cont, Kay Giesecke, Andrei Lopatin, Philipp Schönbucher, Jakob Sidenius, Tolga Uzuner, Yury Volvovskiy and Michael Walker for very helpful discussions. All remaining errors are our own.