Looking Forward to Backward-Looking Rates: Completing the Generalized Forward Market Model

Abstract

In this paper, we show how the generalized Forward Market Model (FMM) introduced by Lyashenko and Mercurio (2019) can be extended to make it a complete term-structure model describing the evolution of all points on a yield curve, as well as of the bank account, and not just of a spanning set of forward term rates. The extended model is both theoretically sound and computationally efficient.

The FMM is an extension of the popular Libor Market Model (LMM), so it can be also used to complete the yield curve evolution under existing LMM implementations.

Keywords: IBOR replacement, LMM, HJM, markovianity, market model, forward rates

JEL Classification: C22, C60, G12, G13