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Dollar and Foreign Zero Rates in FX Forward Pricing

Article Quant Q&A · Author: John
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Summary

The document defines the dollar zero rate and foreign zero rate used in a foreign-exchange forward-pricing expression. The dollar zero rate is the interest rate associated with a dollar-denominated zero-coupon bond. The foreign zero rate is the corresponding rate for a zero-coupon bond denominated in the foreign currency.

These two rates enter the stated forward-price relationship for an FX pair with USD as its base: the spot exchange rate is adjusted over the time to maturity by the exponential of the difference between the dollar and foreign zero rates. The explanation supplies definitions and identifies each rate’s currency denomination, but it does not derive the formula, discuss compounding or day-count conventions, or address collateral and market-specific pricing details. It is a concise terminology clarification rather than a full treatment of FX forward valuation.

Key ideas

  • The dollar zero rate is associated with a dollar-denominated zero-coupon bond.
  • The foreign zero rate is associated with a zero-coupon bond denominated in the other currency.
  • The stated FX forward relationship adjusts spot by the rate difference over the time to maturity.
  • The explanation defines terms but does not derive the pricing formula or discuss market conventions.

Tags

ForexDerivatives pricingFixed income
Full text
# What is the dollar zero rate and the foreign zero rate?


# What is the dollar zero rate and the foreign zero rate?












These terms are used in a proof that the forward price of a foreign exchange pair (where the base is USD) at time $t$ is $X_t \cdot e^{(r_s-r_f)(T-t)}$, where $r_s$ is the dollar zero rate and $r_f$ is the foreign zero rate.

## Answer by Raskolnikov (score 1)

https://quant.stackexchange.com/a/37599

The dollar zero rate is the interest rate of a zero coupon bond issued in dollars. The foreign zero rate is the interest rate of a zero coupon bond issued in the foreign currency.

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.