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 / 100] = 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.
Image and article originally from www.cmegroup.com. Read the original article here.