  We present a detailed analysis of interest rate derivatives valuation under
credit risk and collateral modeling. We show how the credit and collateral
extended valuation framework in Pallavicini et al (2011), and the related
collateralized valuation measure, can be helpful in defining the key market
rates underlying the multiple interest rate curves that characterize current
interest rate markets. A key point is that spot Libor rates are to be treated
as market primitives rather than being defined by no-arbitrage relationships.
We formulate a consistent realistic dynamics for the different rates emerging
from our analysis and compare the resulting model performances to simpler
models used in the industry. We include the often neglected margin period of
risk, showing how this feature may increase the impact of different rates
dynamics on valuation. We point out limitations of multiple curve models with
deterministic basis considering valuation of particularly sensitive products
such as basis swaps. We stress that a proper wrong way risk analysis for such
products requires a model with a stochastic basis and we show numerical results
confirming this fact.
