MODERN LIBOR MARKET MODELS: USING DIFFERENT CURVES FOR PROJECTING RATES AND FOR DISCOUNTING

We introduce an extended LIBOR market model that is compatible with the current market practice of building different yield curves for different tenors and for discounting. The new paradigm is based on modeling the joint evolution of FRA rates and forward rates belonging to the discount curve. We will start by analyzing the basic lognormal case, then we will add stochastic volatility. The dynamics of FRA rates under different measures will be obtained and closed form formulas for caplets and swaptions derived in the lognormal and Heston (1993) cases.