  The market practice of extrapolating different term structures from different
instruments lacks a rigorous justification in terms of cash flows structure and
market observables. In this paper, we integrate our previous consistent theory
for pricing under credit, collateral and funding risks into term structure
modelling, integrating the origination of different term structures with such
effects. Under a number of assumptions on collateralization, wrong-way risk,
gap risk, credit valuation adjustments and funding effects, including the
treasury operational model, and via an immersion hypothesis, we are able to
derive a synthetic master equation for the multiple term structure dynamics
that integrates multiple curves with credit/funding adjustments.
