APPENDIX A

Implying Zero Rates from FX Forward Quotes

In Equation 2.3 we have shown how to obtain a discount factor from an FX forward quote. While approximately correct, the issue is a little more complex. FX forwards are not effective immediately in the sense that the real settlement day is not the moment we agree on the price, but a moment T+n, that is, a number of days n (usually 1, 2, or 3) later.

If we look at Figure 4.5 we see that next to the FX forward quote there is the actual number of days (e.g., we see that six months is precisely 182 days) for which it is valid; this is to ensure a precise calculation.

If we want to create a discount factor for currency X to today (the real definition of present value) we need the combination of USD forward discount factor from the effective settlement date to the maturity of the FX forward and the FX forward itself; this will take us to the effective date. Then we need some interest rate instrument in X to discount from the effective date to today.

Let us collect the information we need:

  • Now is time T (we usually define now as T but here we try to follow the usual notation)
  • The real settlement date T+n
  • The number of days d determining the length of the FX forward
  • The USD forward discount factor (we have usually written a discount factor Di,j without the first suffix denoting the present; here we add it to avoid confusion)

    Unnumbered Display Equation

  • The FX ...

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