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
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: Suggested Citation