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

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