4. Multiple Curve Extensions of Libor Market Models (LMM)

The subject of this chapter are multi-curve models in the spirit of the Libor market model (LMM). The modeling is here done on a discrete tenor structure and the interest rates are discretely compounded, reflecting thus the market practice. We consider the discretely compounded forward OIS rates as reference rates, together with the forward Libor rates or, equivalently, the Libor-OIS spreads. The rates and the spreads are modeled directly under the forward martingale measures used for derivative pricing. First we describe a general framework that extends the classical BGM Libor market model to multiple curves. Then we present a multiple-curve affine Libor model based on families of exponentially affine martingales representing the forward OIS and Libor rates. Finally we also indicate modeling based on multiplicative Libor-OIS spreads. For each modeling approach, we mention corresponding methods for derivative pricing.