Primer: Curve Stripping with Full Collateralisation

In the past five years, it has become clear that there is no longer such a thing as a single "risk-free" interest rate term structure for each currency in the market, and proper pricing of cash ows must take into account basis spreads and collateralisation. An aspect of this issue is considered in this paper: Working in a cross-economy HJM type framework, the Fujii Shimada Takahashi (FST) theorem, specifying the present value of a fully collateralised derivative, is applied to stripping cross-currency swaps. The guiding principle in our approach is that it be based on an underlying arbitrage free interest rate model, in which values of Libors and FX forwards remain invariant under reasonable choices of collateral.