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Estimating FX Forward Points from Cross-Currency Swap Rates

Article Quant Q&A · Author: Robert Jones
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Summary

The document describes how a cross-currency swap can be used to estimate an FX forward rate and express it as forward points relative to spot. One approach first converts the floating currency leg to a fixed rate using the corresponding single-currency swap rate, then converts both legs to zero-coupon rates. Under a simplifying flat-curve assumption, the forward rate follows from the spot rate adjusted by the ratio of the two currencies’ compounded rates over the maturity.

A more general approach uses a pricing curve and swap pricer to value a zero-coupon cross-currency swap with zero initial mark-to-market. The maturity exchange amounts imply the forward FX rate; subtracting spot gives the outright difference, which can then be scaled into points. The simplified calculation depends on assumptions about curves and rates, while accurate conversion requires information about the curves and conventions. The responses outline methods rather than provide a full market-calibrated example.

Key ideas

  • Convert the cross-currency swap legs to comparable zero-coupon rates before deriving the forward rate.
  • A flat-curve assumption allows a simplified estimate using the two currencies’ rates and the spot rate.
  • A swap pricer can derive the forward rate from the maturity exchange amounts of a zero-coupon swap.
  • Forward points represent the difference between the derived forward rate and spot, scaled by market convention.
  • Accurate calculations require curve information and appropriate pricing conventions.

Tags

ForexFixed incomeDerivatives pricing
Full text
# Calculating Fx Swap from Cross Currency Swap


# Calculating Fx Swap from Cross Currency Swap












I am trying to calculate Fx Swap points of a currency pair from the corresponding Cross Currency Swap rate on the same maturity. I.e if I know that my USD/TRY 5Y rate is 16% and my USD/TRY spot rate is 4.62, how can I get the USD/TRY 5Y Fx Swap expressed in points?

Best Regards, Rob

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/41893

You have 16% fixed TRY versus 3mo Usd Libor. Step1: fix out the usd leg using the fair usd swap rate (say 3pct). -> 16% fixed TRY vs 3% fixed USD. Step2: convert these to zero coupon rates. You need information about other points on the curve to do this properly. Assume here that both curves are flat so that zero coupon rates = regular rates ~> 16% zero cpn fixed TRY vs 3% zero cpn fixed usd. Step 4: calculate the forward fx rate = 4.62* ( 1.16/1.03)^5 From which you subtract 4.62 to get the forward points.

## Answer by netbbq (score 0)

https://quant.stackexchange.com/a/41891

If you have cross currency pricing curve and a corresponding swap pricer at hand, you can model a zero coupon cross currency swap, calculate the zero coupon rate on each leg with zero initial MTM. The swap pricer usually provide the accrued interest on each leg at maturity. Adding the par amount of each leg you can get the final exchange amount. The ratio of the two final exchange amount is the forward FX rate. Taking the difference from the spot FX rate and times 10,000, you get the forward points.

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