  We develop a multi-factor stochastic volatility Libor model with
displacement, where each individual forward Libor is driven by its own
square-root stochastic volatility process. The main advantage of this approach
is that, maturity-wise, each square-root process can be calibrated to the
corresponding cap(let)vola-strike panel at the market. However, since even
after freezing the Libors in the drift of this model, the Libor dynamics are
not affine, new affine approximations have to be developed in order to obtain
Fourier based (approximate) pricing procedures for caps and swaptions. As a
result, we end up with a Libor modeling package that allows for efficient
calibration to a complete system of cap/swaption market quotes that performs
well even in crises times, where structural breaks in vola-strike-maturity
panels are typically observed.
