BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS—PART I: PRICING

Authors

  • Stéphane Crépey

    Corresponding author
    1. Université d’Évry Val d’Essonne
    • Address correspondence to Stéphane Crépey, Département de mathématiques, Université d’Évry Val d’Essonne, Laboratoire Analyse et Probabilités, 23 Boulevard de France, 91037 Évry Cedex, France; e-mail: stephane.crepey@univ-evry.fr.

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  • The research of the author benefited from the support of the “Chaire Risque de crédit,” Fédération Bancaire Française. The author thanks Zorana Grbac, Marek Rutkowski, Tom Bielecki, Giovanni Cesari, Jeroen Kerkhof, Jean-Paul Laurent, and Monique Jeanblanc for their involvement at various levels throughout the preparation of this work.

Abstract

This and the follow-up paper deal with the valuation and hedging of bilateral counterparty risk on over-the-counter derivatives. Our study is done in a multiple-curve setup reflecting the various funding constraints (or costs) involved, allowing one to investigate the question of interaction between bilateral counterparty risk and funding. The first task is to define a suitable notion of no arbitrage price in the presence of various funding costs. This is the object of this paper, where we develop an “additive, multiple curve” extension of the classical “multiplicative (discounted), one curve” risk-neutral pricing approach. We derive the dynamic hedging interpretation of such an “additive risk-neutral” price, starting by consistency with pricing by replication in the case of a complete market. This is illustrated by a completely solved example building over previous work by Burgard and Kjaer.

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