Price series for an FX forward contract

Question

Let's assume I am buying a NZD/USD 1Y forward for $1000000 on the 20/02/2017. The NZD/USD 1Y forward point is currently -270 and spot rate is 0.8325. (Example taken from here).

Now I want to have a price return for this at asset at 21/02/2017, 22/02/2017 etc. The 1Y FX forward becomes a 1Y - 1 day, 1Y - 2 days FX forward etc. which are not quoted. So they have to be estimated.

I do have access to the new 1Y FX forward rate on all of those future dates and I also have access to the 6M FX forward rate, 2-Y FX forward rate etc.

How do I create an estimated price series?

Answer 1

Here is an approximate formula requiring no other inputs. Suppose:

$S_0$ = initial spot rate

$F = S_0 + d$ agreed forward exchange rate, where d is the number of forward points

$T$ maturity date of forward

you can calculate an approximate mark-to-market price for the forward on date $t$ $ (0\le t \le T)$ as follows:

$P_t = S_t - (S_0 +d \frac{t}{T})$

Note the following:

$P_0 = 0$. At the moment you enter into the forward agreement you could get out of it with no profit or loss (except perhaps a transaction cost)

$P_T = S_T - F$. This is what textbooks say a forward is worth at maturity. You have made money if the spot rate is above the initially contracted forward rate and have lost money in the opposite case.

When $0<t<T$ the formula gives a linearly interpolated value. This is where the approximation comes in, it is not strictly true, because of interest compounding and for other reasons, but may be close enough for a forward having a maturity of 1 year or less.