3. Multiple Curve Heath–Jarrow–Morton (HJM) Framework

This chapter concerns the HJM framework for forward rate models in a multi-curve setup. As in Chap. 2, also in this chapter we shall model a basic OIS forward rate and the various risky multi-curve rates are obtained by adding a spread over the OIS rate. Since the ultimate goal is the pricing of interest rate derivatives, where the main underlying quantity are the Libor rates, one of the first objectives is to derive models for the dynamics of the Libor rates that are arbitrage-free. To this effect we shall first obtain models for OIS bond prices under a martingale measure and then choose suitable quantities connected to the FRA contracts, modeling them in the spirit of the HJM framework so that the complete model is arbitrage-free. Finally, we consider pricing of linear and optional interest rate derivatives in this HJM context.