The LIBOR Market Model: A Critical Review

Abstract:     
This paper presents a critical review of the different versions of the LIBOR market model (LMM). Based on the new taxonomy of the term structure models (see Nawalkha, Beliaeva, and Soto [2007a, 2007b]) the typical application of the LMM are shown to triple-plus type, exposing these to the dangers of “smoothing.” This paper also derives a double-plus version of Jarrow, Li, and Zhao’s (JLZ) [2007] LMM model with stochastic volatility and jumps, which is less exposed to the dangers of “smoothing” compared with the original triple-plus version of this model. Finally, this paper makes a persuasive case for considering high-dimensional double-plus term structure models in the affine and quadratic classes. Fast computational methods make these models powerful alternatives to the LMM for valuing and hedging interest rate derivatives.

Keywords: LIBOR market model, affine and quadratic models, interest rate models, caps, swaptions

JEL Classifications: G10, G11, G12, G13, G21, G22, G23

Working Paper Series