Discounting FX Forward Mark-to-Market Cash Flows

Summary

The document addresses how to value an existing FX forward by imagining an offsetting forward that leaves a net future cash flow in one currency. Its central point is that the appropriate discount rate depends on the collateral arrangement. For dollar cash collateral remunerated at SOFR, one approach is to offset the non-dollar amounts and discount the remaining dollar cash flows at SOFR.

Alternatively, the dollar amounts can be offset, leaving a local-currency cash flow discounted using a local rate adjusted for the currency basis. The answer says these approaches should produce the same valuation. This illustrates that the domestic interest rate swap curve alone may not be appropriate when cross-currency basis affects the relevant funding relationship. The explanation assumes a specified collateral setup and explicitly sets collateral questions aside in the original query; results should not be applied without matching the valuation method to the actual collateral terms and market conventions.

Key ideas

• The collateral terms determine the discount rate used to value FX forward cash flows.
• Offsetting non-dollar amounts leaves dollar cash flows that can be discounted at the collateral rate.
• Offsetting dollar amounts instead requires a basis-adjusted local-currency discount rate.
• Both cash-flow representations should yield the same valuation under consistent assumptions.

Tags

# Marking an FX Forward Position


# Marking an FX Forward Position












I understand that one simple way to calculate the present value of an fx forward position is to assume an offsetting transaction at the current market price and discount the (future) 'net' cash flow back to the present.

Suppose that you have a 1yr fx forward position, and you assume an offsetting transaction that exactly matches its USD notional. Then, you'd be left with a net cash flow in a local currency due in one year, which then can be simply discounted to the present to derive its valuation.

My question is, in discounting this future (net) cash flow in local currency, which curve do you need to use? A domestic IRS curve? or a CCS curve that reflects the cross currency basis b/w the local currency and USD? (let's not consider the collateral issue here for simplicity)

Given that the choice of the curve impacts the valuation of the fx forward position, can you advise what would be the correct method in this case? (or is market practice at least?)

## Answer by dm63 (score 5, accepted)

https://quant.stackexchange.com/a/82226

The collateral determines the discount rate. For example if the collateral is dollar cash paid at SOFR , the the correct procedure is either (a) match off the non dollar amounts leaving only dollar cashflows, which can be discounted at SOFR or (b) match off the dollar amounts leaving a non dollar amount which must be discounted at a currency basis adjusted local currency rate. Those should give the same answer.

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