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Marking an FX Forward Using the Remaining-Term Forward Rate

Article Quant Q&A · Author: Phil-ZXX
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Summary

The discussion explains how to mark a USDJPY forward before maturity. For a position that receives dollars and pays yen at a contracted strike, the offsetting transaction uses the current forward rate for the remaining term, rather than spot. That remaining-term forward rate reflects the current market rate at which the position could be closed out for the same expiry.

The example’s proposed valuation expresses the cash-flow difference in dollars and discounts it with the USD discount factor for the remaining tenor. The answer explains that dollar discounting applies because the value is being expressed in dollars; converting the yen amount at the relevant forward rate gives its dollar equivalent. This is a concise explanation of the stated setup, not a general treatment of collateral, discounting conventions, settlement details, or cross-currency basis, which can matter in practical valuation.

Key ideas

  • Mark an outstanding FX forward against the market forward rate for its remaining tenor.
  • The remaining-term forward rate represents the rate for an offsetting trade with the same expiry.
  • Use the discount factor for the currency in which the present value is expressed.
  • The yen cash flow is converted to a dollar equivalent when forming the dollar value.
  • Practical valuation conventions may depend on collateral and market details not covered here.

Tags

ForexFixed incomeDerivatives pricing
Full text
# MtM of FX Forward


# MtM of FX Forward












I had a look at pnl calculation of FX forward but it didn't quite match my question.

Say $X_{t,\tau}$ is the USDJPY FX Forward Rate as seen at time $t$ for expiry $t+\tau$. So $X_{t}^{spot} := X_{t,0}$ can be understood as "Spot" at time $t$.

- At time $t=0$ (today), I enter into a 12M FX Forward on USDJPY at the fair strike of $$K=X_{0,12M}=110$$ That is, in 1 year I receive 1 USD and pay 110 JPY. No money changes hands, because the trade's PV is zero at inception.

- At time $t=3M$ (i.e. 3 month later), FX rates have moved and I want to know what my trade's PV is. Which one is correct:

$$\text{PV in USD} = \left(1 - \frac{K}{X_{3M}^{spot}}\right) \cdot D_{9M}^{USD}$$ $$\text{or}$$ $$\text{PV in USD} = \left(1 - \frac{K}{X_{3M,9M}}\right) \cdot D_{9M}^{USD}$$

Two questions:

- Do I use Spot or the 9M-Fwd to compute my PV/PnL? The 9M-Fwd seems more correct to me, because that's the rate I'd use to close out my position.

- Is my use of the USD discount factor $D_{9M}^{USD}$ correct? I am asking because it seems like I have no direct exposure to JPY rates when calculating my PV this way.

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/40097

You are correct on both questions. 1 you answered yourself. It is the correct rate to close out the trade. 2 you use a dollar discount rate because you are discounting dollars. The (1-K/X) term represents one dollar from the first trade and K/X dollars from the close out trade.

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