Multi-Curve Modeling Using Trees

27 Pages Posted: 3 May 2015 Last revised: 18 Sep 2017

See all articles by John C. Hull

John C. Hull

University of Toronto - Rotman School of Management

Alan White

University of Toronto - Rotman School of Management

Date Written: November 8, 2015

Abstract

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 modeled 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.

Keywords: OIS, LIBOR, interest rate trees, multi-curve modeling

JEL Classification: G10, G12, G13

Suggested Citation

Hull, John C. and White, Alan, Multi-Curve Modeling Using Trees (November 8, 2015). In Innovations in Derivatives Markets, edited by Kathrin Glau, Zorana Grbac, Matthias Scherer, and Rudi Zagst, SpringerProceedings in Mathematics and Statistics, 2016: 171-189. Available at SSRN: https://ssrn.com/abstract=2601457

John C. Hull (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada
(416) 978-8615 (Phone)
416-971-3048 (Fax)

Alan White

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada
416-978-3689 (Phone)
416-971-3048 (Fax)

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