Libor Transition: Looking Forward to Backward-Looking Rates

Abstract: In this talk, 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 that of the bank account. The ability to model the bank account, in addition to the forward curve, is going to be of crucial importance once Libor rates are replaced with setting-in-arrears risk-free rates in derivative and cash contracts, where fixings are defined in terms of the realized bank account values.

To obtain the evolution of all points on the yield curve, we embed the FMM into a (finite-dimensional) Markovian Heath-Jarrow-Morton (HJM) model with separable volatility structure by aligning the HJM and FMM dynamics of the forward term rates modeled by the FMM. This FMM-aligned HJM model is effectively a hybrid between an instantaneous forward-rate model and a LMM, and shares the advantages of both approaches, with the caveat that the number of variables to simulate could be too high. A more efficient approach is then derived by expressing the price of an arbitrary zero-coupon bond, as well as the bank account, as a function of the modeled forward term rates and their volatilities.