Cross Currency Swaption

A Cross Currency European Swaption is a European Swaption to enter into a swap to exchange cash flows in two different currencies. The domestic and foreign swap leg cash flows can be fixed or floating. The model outlined here is called a Multi-Currency Terminal Swap Rate Model which generalizes a Terminal Swap Rate Model to incorporate foreign exchange. The main idea behind a Terminal Swap Rate Model is to assume that the discount factors at the option maturity can be written as a function of the underlying swap rates. This assumption reduces the number of stochastic variables that need to be modelled.

A Cross Currency European Swaption gives the holder the option to enter into a swap to exchange cash flows in two different currencies. The domestic and foreign swap leg cash flows can be fixed or floating.

The underlying cross-currency swap can be fixed-to-fixed, fixed-to-floating and floating-to-floating types with possible floating spread and principal exchanges which may happen at the beginning of the swap or at the end of the swap or at both the beginning and the end. The floating index interest rate for the CAD is BA rate and the one for USD is the LIBOR rate. In this swaption, the BA-LIBOR basis spread is also considered.

Even for a European cross-currency swaptions, a number of enforced assumptions have to be introduced to reduce the complexity of the problem. Some of the assumptions are purely technical and some of them are supported by historical observations. One of the technical assumptions is that PVBPs for both currencies at a swaption maturity can be approximated by the corresponding forward PVBPs.

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