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An Overview of the Valuation of Collateralized Derivative Contracts

by Jean-Paul Laurent of Université Paris 1 Panthéon-Sorbonne,
Philippe Amzelek of BNP Paribas, and
Joe Bonnaud of BNP Paribas

October 2012

Abstract: We consider the valuation of collateralized derivative contracts such as interest rate swaps, forward FX contracts or term repos. First, we provide a precise framework regarding collateralization, under which computations are made easy. We allow for posting securities or cash in different currencies. In the latter case, we focus on using overnight index rates on the interbank market, in line with LCH.Clearnet framework. We provide an intuitive way to derive the basic discounting results, keeping in line with the most standard theoretical and market views. Under perfect collateralization, pricing rules for collateralized trades remain linear, thus the use of (multiple) discount curves. We then show how to deal with partial collateralization, involving haircuts, asymmetric CSA, counterparty risk and funding costs as an extension of the perfect collateralization case. We therefore intend to provide a unified view. Mathematical or legal details are not dealt with and we privilege financial intuition and easy to grasp concepts and tools.

JEL Classification: G01, G12, G33.

Keywords: collateral management, clearing house, CSA, haircuts, swaps, repos, OIS.

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