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Valuing the Remaining P&L of a Settled FX Swap

Article Quant Q&A · Author: Philipp Rott
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Summary

The document explains how to measure profit and loss on an FX swap after its near leg has settled. The remaining forward still has value, while the currency received or delivered on settlement remains an asset or liability exposed to spot movements. For an equal-notional swap, those opposing spot exposures offset, so the P&L can be calculated from the change in forward points to the far date, discounted in the trader’s functional currency.

A EUR/USD example illustrates the idea: after settlement, the trader is long EUR and short EUR forward. A rise in spot benefits the currency holding but worsens the forward position; considering both legs gives the full P&L. The shortcut captures their net effect through the forward-point change. It applies only when near- and far-leg notionals match. With unequal notionals, spot exposures do not cancel, and each leg must be valued using its own notional.

Key ideas

  • After near-leg settlement, account for both the remaining forward and the asset or liability created by settlement.
  • Equal notionals make the two legs’ spot exposures offset.
  • For an equal-notional swap, P&L can be expressed using the change in forward points, discounted in the functional currency.
  • Unequal notionals leave residual spot exposure, so each leg requires separate valuation.

Tags

ForexDerivatives pricingRisk management
Full text
# FX Swap PnL and NPV


# FX Swap PnL and NPV












Suppose I have an existing FX Swap, suppose the spot leg is already settled, so only forward leg is left.

Question: What will be the P&L for this instrument - only forward leg NPV or spot leg is also marked-to-market to current spot rate?

Thanks a lot!

## Answer by AlRacoon (score 3)

https://quant.stackexchange.com/a/71060

While the near leg is settled, in order to get the full PnL of the trade, you will value the remaining leg of the swap, as well as asset from the settled leg. However, there is a short cut as the settled short leg is valued at spot and the remaining long leg is valued at spot + forward points. Since the settled short leg and the remaining long leg are opposite direction on spot, you only need to value the change in the forward points to your long leg date and discount at the discount rate in your functional currency. (ie. spot is negated).

To illustrate:

In an fx swap, you will buy (or sell) a foreign currency at a near date and simultaneously sell (or buy) that foreign currency at a further date.

To make the fx swap simple (and create the scenario of the OP), let's just say the near date is spot and the far date is 1 month from now. And the foreign currency is EUR and the base currency is USD. And the direction is the trader is buying EUR spot and selling EUR 1 month out. Let's assume spot EUR = 1 USD and the forward was traded at +0.10 USD forward points.

Upon settlement of the trade, the trader is now Long 1 EUR at 1 USD and Short 1 EUR 1M forward at 1.1 USD.

Say 1 week passes and the EUR has now moved to 1.1 USD and the 3 week forward is trading at spot + 0.11.

The trader is now long 1 EUR valued at 1.1 USD and short a 3 week EUR forward at 1.1 when the market is 1.21 (1.1 + 0.11 USD forward points). The full PnL would be an appreciation of long EUR and the loss on the now 3 week forward. One could value each of these legs by discounting these rates (obviously spot EUR would not be discounted).

Alternatively, since the long EUR and the short EUR forward are both exposed to spot in opposite directions, the remaining leg of the swap could be valued at the discounted value of just the change in the forward points.

Important: this can only be done if it is an even fx swap (the notional of the near leg and the far leg are the same). In real life, the fw swap is often an uneven swap and the individual legs will need to be valued according to the notional of each leg. The spot exposures will not net out since the notionals are different on the near and far legs of the swap.

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.