Pricing Interest Rate Derivatives and Computing Pathwise Greeks in the Extended LIBOR Market Model

Abstract

Classical interest rate models were formulated under the no-arbitrage assumption of a unique yield curve. However, in the outbreak of the 2007 global financial crisis, market interest rates witnessed unprecedented segmentation, and this instigated the modelling of a basis spread, whose non-negligible widening could no longer be neglected. One extension of the LIBOR market model (LMM) to incorporate basis spread was proposed by Mercurio (2010a), and in this paper, we examine how his theoretical description is translated into practical implementation to price interest rate derivatives and compute pathwise Greeks. Specifically, our contribution is to develop and implement the theory of the extended LMM in the framework of a displaced diffusion process in the spot LIBOR measure. The adjoint mode from algorithmic differentiation is premiered in this new implementation to compute pathwise deltas and vegas before the accumulated knowledge is applied in the pricing of interest rate caps and one-way floaters.