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Approximating Mark-to-Market Returns for FX Forward Contracts

Article Quant Q&A · Author: Joachim
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Summary

This note gives a simple way to estimate the mark-to-market value of an existing FX forward between its trade date and maturity. It linearly interpolates the agreed forward rate from the initial spot rate toward the contracted maturity rate, then compares that interpolated rate with the current spot rate. At inception the estimate is zero, while at maturity it becomes the difference between current spot and the contracted forward rate, with the sign indicating gain or loss for the stated orientation.

The method is offered as an approximation that requires no additional market inputs. It does not fully revalue the contract using current forward curves, interest-rate differentials or compounding conventions, so it may be less accurate as time passes or for longer maturities. The note says it may be adequate for forwards with maturities of a year or less, but provides no empirical comparison or error analysis.

Key ideas

  • The estimate compares current spot with a linearly interpolated contracted forward rate.
  • It starts at zero value on the trade date and reaches spot minus the contracted rate at maturity.
  • The interpolation approximates the mark-to-market path between those endpoints.
  • Interest compounding and other effects are omitted, limiting accuracy.

Tags

ForexDerivatives pricing
Full text
# Price series for an FX forward contract


# Price series for an FX forward contract












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 by nbbo2 (score 1, accepted)

https://quant.stackexchange.com/a/36064

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.