The Valuation of Fixed Term Securities Lending in a Multi-Curve Framework

Abstract

We consider the risk neutral valuation of fixed term securities lending in a multi-curve framework, taking into account the forward basis of each component of the transaction relative to the discount curve, including basis between currencies. We show that a convexity adjustment arises from the collateral basis being applied to an unnatural notional proportional to the lent security price rather than to the collateral instrument(s) price(s). In practical cases the convexity adjustment is small and can be safely ignored.

Keywords: fixed term securities lending, securities lending, repo, multi-curve, basis, convexity adjustment

JEL Classification: G10, G12, G13