Linking caplets and swaptions prices in the LMM-SABR model

Riccardo Rebonato and Richard White

Journal of Computational Finance

Abstract: ABSTRACT We use (and improve upon) a recent time-homogeneous extension of the stochastic alpha beta rho (SABR)-LIBOR market model (LMM) approach described in Rebonato (2007) to develop a quick and accurate analytical approximation to the implied swaption prices given the forward-rate SABR-LMM parameters. This approximation can be used for studies of calibration of a forward-rate-based LMM-SABR model to (portions of) the swaption matrix, to determine the constant maturity swap (CMS) drift corrections (see Hagan (2003)) and to study the congruence between the caplet and swaption markets.

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