Forward points follow from two money market rates
Table of Contents
1. Summary
Given spot and one money market rate per currency, the forward has a closed form. The form inverts to give either rate from the points.
2. Detail
\[F = S \times \frac{1 + r_q \frac{N}{B_q}}{1 + r_b \frac{N}{B_b}}\]
\(r_b\) and \(r_q\) are the rates of the base and quote currencies, \(N\) the days, and \(B_b\) and \(B_q\) the day-count bases of each rate. The bases can differ, such as ACT/360 for USD and ACT/365 for JPY. The points are \((F - S)\) divided by the pip factor.
Solving for the quote currency rate:
\[r_q = \frac{B_q}{N} \left[ \frac{F}{S} \left( 1 + r_b \frac{N}{B_b} \right) - 1 \right]\]
The growth factors are inverse discount factors, so this is the discrete form of Covered Interest Parity and FX Forward Pricing. The unit tests of fx_forward_calculator hold both directions.
3. See also
- FX forwards — the structure note.
- Forward points are the difference between the outright and spot — completes: the quantity this gives.
- Covered Interest Parity and FX Forward Pricing — exemplifies: parity on discrete rates.
- An FX-implied curve is backed out from a discount curve and forward points — completes: the same inversion over a whole curve.