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Multi-Curve Modeling Using Trees

Since 2008 the valuation of derivatives has evolved so that OIS discounting rather than LIBOR discounting is used. Payoffs from interest rate derivatives usually depend on LIBOR. This means that the valuation of interest rate derivatives depends on the evolution of two different term structures. The spread between OIS and LIBOR rates is often assumed to be constant or deterministic. This paper explores how this assumption can be relaxed. It shows how well-established methods used to represent one-factor interest rate models in the form of a binomial or trinomial tree can be extended so that the OIS rate and a LIBOR rate are jointly modelled in a three-dimensional tree. The procedures are illustrated with the valuation of spread options and Bermudan swap options. The tree is constructed so that LIBOR swap rates are matched.