Bergman, Piterbarg and Beyond: Pricing Derivatives under Collateralization and Differential Rates

19 Pages Posted: 17 Sep 2013 Last revised: 18 Dec 2013

Date Written: December 2013

Abstract

We extend Piterbarg's (2010) result on European-style derivative pricing under collateralization by relaxing the assumption of a single unsecured funding rate. Introducing different lending and borrowing rates has the effect of producing non-linear price functionals for general claims. Buyer and seller prices diverge, and values of derivative portfolios are not the sum of the individual deal values. Conditions under which no-arbitrage price bounds can be derived explicitly are given and numerical examples show-cased.

Keywords: Derivatives pricing, collateralization, funding, differential rates, no-arbitrage bounds

JEL Classification: C60, G13

Suggested Citation

Mercurio, Fabio, Bergman, Piterbarg and Beyond: Pricing Derivatives under Collateralization and Differential Rates (December 2013). Available at SSRN: https://ssrn.com/abstract=2326581 or http://dx.doi.org/10.2139/ssrn.2326581

Fabio Mercurio (Contact Author)

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

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