FX Forward Pricing from Covered Interest Parity and Cross-Currency Basis
Summary
The document derives a simple FX forward relationship from covered interest parity. For two currencies, it compares converting at spot and investing at the domestic rate with investing at the foreign rate and locking in the maturity conversion rate through a forward. In the frictionless argument, the two strategies must have equal maturity values to prevent arbitrage, relating spot, forward, and the two interest rates.
It then explains that observed forward quotes may depart from this simple parity, with the cross-currency basis represented as an adjustment to one currency's rate. The answer attributes persistent deviations since 2008 to funding demand imbalances and limited bank capacity to intermediate arbitrage flows, especially demand for USD funding. This is an intuitive explanation and a simplified one-year setup; it does not provide the requested reference paper or explain practical curve calibration, conventions, compounding, or tenor-specific basis construction.
Key ideas
- Covered interest parity equates the maturity values of two currency investment routes when the forward rate is locked in.
- The simple relationship links spot, forward, and domestic and foreign interest rates.
- A cross-currency basis adjusts the parity relationship to reflect market forward pricing.
- Funding imbalances and constrained arbitrage capacity are offered as reasons for persistent basis deviations.
- The answer gives no reference paper or detailed procedure for calibrating an FX forward curve.
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Full text
# Fx forward Formula with CBS
# Fx forward Formula with CBS
I'd like to know how we get the below formula that represents the theoretical pricing of a foreign exchange (FX) forward contract, incorporating adjustments for domestic and foreign interest rates as well as the cross-border spread (CBS). Pease provide any reference paper for that formula, and how it's used to calibrate Fx forward curve Thanks
## Answer by user68819 (score 3)
https://quant.stackexchange.com/a/81446
The CIP theory:
If I have 1 EUR today I can (assuming a 1y term to keep notation simple):
a). convert it into USD at a spot rate of $S$ and deposit that money in a USD bank account for 1 year. I will have $S(1+r_{usd})$ at maturity.
b). I can lend this money to an EU bank and earn $(1+r_{eur})$ and convert this at maturity to USD. I can lock that rate in today at an exchange rate of $F$. Giving me $F(1+r_{eur})$ in 1y time.
The two must be equal to preclude arbitrage. Therefore:
$S(1+r_{usd}) = F(1+r_{eur})$, this is also known as the simple covered interest rate parity (sCIP).
The market reality:
In the market what tends to happen, is that despite the above arguments you might still not match the price of quoted forwards. And this has been observed consistently since 2008. Why? As there tends to be an excess demand for 1 currency over another, and the capacity of banks to arbitrage huge international flows is limited, typically participants will pay a premium to get USD funding and this manifests as the "basis". By definition the Xccy basis is precisely the adjustment made (by convention on the non-USD leg of the trade) to allow you to be able to get to the market price of the FX Fwds.
In this case $S(1+r_{usd}) = F(1+r_{eur}+Xccy\_basis)$
So the CIP equation has had to be modified by the addition of this "extra term" the Xccy basis. It is no longer quite so "simple".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.