  For a long time interest-rate models were built on a single yield curve used
both for discounting and forwarding. However, the crisis that has affected
financial markets in the last years led market players to revise this
assumption and accommodate basis-swap spreads, whose remarkable widening can no
longer be neglected. In recent literature we find many proposals of multi-curve
interest-rate models, whose calibration would typically require market quotes
for all yield curves. At present this is not possible since most of the quotes
are missing or extremely illiquid. Thanks to a suitable extension of the HJM
framework, we propose a parsimonious model based on observed rates that deduces
yield-curve dynamics from a single family of Markov processes. Furthermore, we
detail a specification of the model reporting numerical examples of calibration
to quoted market data.

Pricing of Securities