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Keywords:

  • funding;
  • collateral;
  • derivatives;
  • OIS discounting;
  • FVA;
  • replication cost

Abstract

In this note we show that the inclusion of funding costs and collateralization into the valuation of derivatives (via replication) is analogue to the modelling of cross-currency and quantoed claimes, where the role of the FX process is taken by a “fund exchange process”. Hence, classical cross-currency (alternatively risky curve models) may be used to construct rich models for (stochastic) funding. In an appendix we make two remarks motivating the use of a dedicated funding curve.