Lévy forward price approach for multiple yield curves in presence of persistently low and negative interest rates

In this talk we present a framework for discretely compounding
interest rates which is based on the forward price process approach.
This approach has a number of advantages, in particular in the current
market environment. Compared to the classical Libor market models, it
allows in a natural way for negative interest rates and has superb
calibration properties even in the presence of persistently low rates.
Moreover, the measure changes along the tenor structure are simplified
significantly. This property makes it an excellent base for a
post-crisis multiple curve setup. Two variants for multiple curve
constructions will be discussed.

As driving processes we use time-inhomogeneous Lévy processes, which
lead to explicit valuation formulas for various interest rate products
using well-known Fourier transform techniques. Based on these formulas
we present calibration results for the two model variants using market
data for caps with Bachelier implied volatilities.