A Libor market model including credit risk under the real-world measure

We present a methodology to generate future scenarios of interest rates for different credit ratings under a real-world probability measure. More precisely, we explain how to perform simulations of the real-world forward rates for different rating classes by generalizing the multidimensional shifted lognormal London Interbank Offered Rate market model to account for credit ratings and a specification of the market prices of risk vector processes. The proposed methodology allows for the presence of negative interest rates, as currently observed in the markets, and guarantees the monotonicity of forward rates with respect to credit ratings.