Libor Market Model with Regime-Switching Volatility

This paper provides regime-switching stochastic volatility extensions of the LIBOR market model. First, the instantaneous forward LIBOR volatility is modulated by a continuous time homogeneous Markov chain. In a second parameterization, the volatility is modelled by a square root process with a regime-switching reference level. We obtain analytical solutions for the prices of caplets in this setting as well as approximations for the prices of swaptions. The model is illustrated by some popular parametric volatility specifications. The generator of the chain can be easily estimated by using implied volatility data from caps, floors and swaptions.