The geometry of multi-curve interest rate models

Abstract: We study the problems of consistency and of the existence of finite-dimensional realizations for multi-curve interest rate models of Heath-Jarrow-Morton type, generalizing the geometric approach developed by T. Bj\"ork and co-authors in the classical single-curve setting. We characterize when a multi-curve interest rate model is consistent with a given parameterized family of forward curves and spreads and when a model can be realized by a finite-dimensional state process. We illustrate the general theory in a number of model classes and examples, providing explicit constructions of finite-dimensional realizations. Based on these theoretical results, we perform the calibration of a three-curve Hull-White model to market data and analyse the stability of the estimated parameters.