20 Pages Posted: 16 Apr 2012
Date Written: April 16, 2012
Given a forwarding LIBOR-style curve F corresponding to a fixed tenor (e.g. 6m) and an exogenous discounting curve D (e.g. an OIS curve or cross-currency basis swap curve) we build on Bianchetti's results to propose dynamics for the forward LIBOR-style rate collateralized by D.
In contrast with what other authors do (Bianchetti, Mercurio, Fujii, et al.) we do not assume that the collateralized forward rate is a martingale process under the corresponding forward risk neutral measure associated with the discount process. At time zero the collateralized forward rate is the forwarding curve rate multiplied by a quanto adjustment, but at reset time the expectation of the collateralized forward aligns with the forwarding curve rate.
In order to calculate the quanto adjustment we show how to construct a deterministic drift, which can be computed with the information available at time zero by bootstrapping (under certain assumptions on the spot swap rates). We extend the result to forward swap rates in the context of swap market models.
Keywords: non-martingale, two curve framework, multi-curve, collateralized forward rates, curve bootstrapping, multiple yield curves, forward curve, discount curve, basis adjustment, quanto adjustment, swap market models, LIBOR market models, interest rate derivatives, FRAs, swaps, swaptions, overnight index
JEL Classification: E43, G12, G13
Suggested Citation: Suggested Citation
By Marc Henrard
By Ilya Gikhman