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CME Group has developed a tool to calculate, in real-time, the magnitude of EUR/USD cross-currency basis for short-dated periods and forward-starting IMM periods.

## What is cross-currency basis?

We define cross-currency basis as the difference in value between 1) the exchange price of a FX forward contract and 2) the theoretical price of the same FX forward contract according to covered interest parity, derived from the current spot price and the individual interest rates of the two currencies involved in the forward contract (in this case, USD and euro). For a primer on the calculation, please see this paper.

Cross-currency basis can be expressed for any FX forward date out of spot or for forward-starting periods known as forward-forwards. The CME Group tool shows levels for consecutive forward-starting IMM dated periods.

Cross-currency basis is typically expressed in terms of basis points on the interest rate of the non-dollar currency. We conform to this norm. For example, if cross currency basis in a specified period for EUR/USD is quoted at -22bp, that can be interpreted as meaning that the forward FX swap points, known as pips, are equal to the pips implied by the benchmark USD interest rate and the benchmark EUR interest rate less 22bp for that specified period.

## How the tool works

The CME Group Cross-Currency Basis Watch uses prices from the following sources:

• Three-month SOFR Futures contracts (SR3)
• Three-month ESTR Futures contracts (ESR)
• EUR/USD FX Futures contracts (6E)

For both SR3 and ESR Interest Rate futures, the contract represents the level of expected interest over the reference period. For example, the June 23 named contract runs from the June IMM date (June 21, 2023) to the September IMM date (Sep. 20, 2023). Please see here and here for detailed explanations of how the final settlement price of SR3 and ESR is determined by the compounded accrual of the relevant interest rates over the reference periods. Interest Rate futures are quoted in price, where the price is equal to 100 less the implied rate of interest over the period. A price of 96.54 represents an expected level of interest rate at 3.46%.

In contrast to Interest Rate futures, FX futures represent a price at a point in time. Each 6E contract represents a forward outright price on its value date, whereby value dates are defined by the IMM calendar as the third Wednesday of each quarterly month – March, June, September, and December. Consequently, the difference between two consecutive quarterly 6E contracts represents the forward points between their respective value dates.

CME FX Link is a product that links OTC FX with nearby FX futures. The traded price represents the basis between OTC spot FX and CME FX futures. Our FX spot price is calculated by reference to the nearest quarterly 6E contract combined with the value of FX Link to that value date, whereby the spot price is the futures price less the link price. This calculation of spot pricing is supported by the observation in this BIS report that FX futures are increasingly a primary source of price discovery in the foreign exchange market.

### Calculating forward-forward basis - An example: June 2023

Using covered interest parity as described by this formula:

F = The forward foreign exchange rate
S = The Spot foreign exchange rate
id = The domestic interest rate
if = The foreign interest rate

The forward foreign exchange swap rate is determined by subtracting the spot rate (S) from the forward rate (F), hence the forward swap = F - S. While S refers to the spot rate in this formula, in practice it can also be a forward rate provided F designates a longer-dated forward rate, thus allowing the pricing of forward swaps from any forward date to any other longer-dated forward date. Note that EUR/USD is quoted with EUR as the domestic currency and USD as the foreign currency.

We will review a hypothetical forward-forward beginning on the June 2023 IMM date and ending on the Sep. 2023 IMM date:

Contract description Reference period start Reference period end Code Price Interest rate
Three-month SOFR - June 2023 June 21, 2023 Sep. 20, 2023 SR3M3 94.7175 5.2825
Three-month €STR - June 2023 June 21, 2023 Sep. 20, 2023 ESRM3 96.4975 3.5025
Value date     Implied Fwd points
EUR/USD FX
June 2023
June 21, 2023 6EM3 1.0747
EUR/USD FX September 2023 Sep. 20, 2023 6EU3 1.080175 54.75

There are 91 days between the IMM dates in our example hence the respective interest rates will apply for 91/360 days.

Beginning with 1 Euro we would have:

(1 + 3.5025% x 91/360) x 1 = 1.008854

and beginning with 1.0747 USD (from the starting FX outright price) we would have:

(1 + 5.2825% x 91/360) x 1.0747 = 1.08905

Thus, we arrive at:

1.008854 EUR = 1.08905 USD and dividing both sides by the EUR amount:

1 EUR = 1.07949 USD at the forward date of 20-Sep-23

That is the forward exchange rate implied by the SOFR and ESTR futures

The implied forward pips are thus: 1.07949 - 1.0747 = 0.00479 or 47.9 pips

From the EUR/USD FX contracts we also have a measure of the forward points at 54.75 pips, by keeping all other variables constant we can solve for the theoretical ESTR interest rate that would imply 54.75pips.

In this case we are solving for:

1 EUR = 1.080175 USD where 1.0747 + 0.005475 = 1.080175

Given that the USD rate is held constant:

1.08905 / 1.080175 = 1.008217 EUR

Implies a Euro interest rate of:

[(1.008217 -1) x 360 / 91] = 3.25056%

Comparing the implied rate with the original observed EUR rate we have:

3.25056 - 3.5025 = -25.194 bp

Thus, we have calculated the implied Cross Currency basis for the period from 21-Jun-23 to 20-Sep-2023

The tool continues to calculate each forward-forward period generating an implied Cross Currency Basis value for each period displayed in the column to the right-hand side.

## Disclaimer

The data and output from this tool does not constitute investment advice and is not a personal recommendation from CME Group.  Nothing contained herein constitutes the solicitation of the purchase or sale of any futures or options.  Any investment activities undertaken using this tool will be at the sole risk of the relevant investor.  CME Group expressly disclaims all liability for the use or interpretation (whether by visitor or by others) of information contained herein. Decisions based on this information are the sole responsibility of the relevant investor.  Any visitor to this page agrees to hold the CME Group and its affiliates and licensors harmless against any claims for damages arising from any decisions that the visitor makes based on such information. CME Group does not warrant the accuracy or completeness of the information produced by this tool.

## EUR/USD Cross-Currency Basis Monitoring tool

Use the CME Cross-Currency Tool to find the implied cross-currency basis for short-dated periods and forward-starting IMM periods.

All examples in this report are hypothetical interpretations of situations and are used for explanation purposes only. The views in this report reflect solely those of the author and not necessarily those of CME Group or its affiliated institutions. This report and the information herein should not be considered investment advice or the results of actual market experience.

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