An Efficient Lattice Algorithm for the Libor Market Model

31 Pages Posted: 26 Aug 2011 Last revised: 25 Sep 2011

Tim Xiao

Risk Models, BMO Capital Markets

Date Written: June 18, 2011

Abstract

The LIBOR Market Model (LMM or BGM) has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice (or tree) approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround.

Keywords: LIBOR Market Model, LMM lattice or tree, BGM lattice or tree, shifted forward measure, drift approximation, risk management, calibration, callable exotics, callable bond, callable capped floater swap, callable inverse floater swap, callable range accrual swap

JEL Classification: G1, C5, C6, F1

Suggested Citation

Xiao, Tim, An Efficient Lattice Algorithm for the Libor Market Model (June 18, 2011). Journal of Derivatives, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1916369

Tim Xiao (Contact Author)

Risk Models, BMO Capital Markets ( email )

Canada

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