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Up and Down Credit Risk

by Tom Bielecki of Illinois Institute of Technology,
Stéphane Crépey of the Université d' Évry Val d'Essonne, and
Monique Jeanblanc of the Université d' Évry Val d'Essonne & Europlace Institute of Finance

October 1, 2009

Abstract: This paper discusses the main modeling approaches that have been developed so far for handling portfolio credit derivatives. In particular the so called top, top down and bottom up approaches are considered. We first provide an overview of these approaches. We give some mathematical insights to the fact that information, namely, the choice of a relevant model filtration, is the major modeling issue. In this regard, we examine the notion of thinning that was recently advocated for the purpose of hedging a multi-name derivative by single-name derivatives. We then give a further analysis of the various approaches using simple models, discussing in each case the issue of hedging. Finally we explain by means of numerical simulations (semi-static hedging experiments) why and when the portfolio loss process may not be a sufficient statistics for the purpose of valuation and hedging of portfolio credit risk.

Keywords: credit risk, credit derivatives, filtration, thinning, hedging.

Published in: Quantitative Finance, Vol. 10, No. 10, (October 2010), pp. 1137-1151.

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