We develop a multi-curve term structure setup in which the modelling
ingredients are expressed by rational functionals of Markov processes. We
calibrate to LIBOR swaptions data and show that a rational two-factor lognormal
multi-curve model is sufficient to match market data with accuracy. We
elucidate the relationship between the models developed and calibrated under a
risk-neutral measure Q and their consistent equivalence class under the
real-world probability measure P. The consistent P-pricing models are applied
to compute the risk exposures which may be required to comply with regulatory
obligations. In order to compute counterparty-risk valuation adjustments, such
as CVA, we show how positive default intensity processes with rational form can
be derived. We flesh out our study by applying the results to a basis swap
contract.Comment: 34 pages, 9 figure
