Rate gaps and FX forwards: the parity maths with official rates

Where the five official rates stand

Each rate below was fetched on 21 October 2026 from the bank’s own data series, the same series our central bank tracker at /central-banks reads. The “in force since” date is the first day of the current level in that series, and the “previous” column is the level immediately before it.

The pattern is a split. The Federal Reserve raised its target range by 25 bp to 3.75–4.00%, effective 17 September 2026, and the ECB raised its deposit facility rate by 25 bp to 2.50%, effective 16 September 2026, its second increase of the year after a move from 2.00% to 2.25% effective 17 June 2026. The Bank of England, Bank of Canada and Swiss National Bank all last moved by cutting, in 2025, and have held since.

The gaps against the dollar

A rate differential is one rate minus the other. The Fed sets a range rather than a single rate, so we use its midpoint, 3.875% (our calculation: (3.75 + 4.00) ÷ 2), and give the gap against the edges of the range in brackets.

Two details stand out. First, the EUR/USD gap did not change in September: both banks raised by 25 bp within two days of each other, so the gap stayed at 137.5 bp. The last time it changed was 17 June 2026, when the ECB’s increase narrowed it from 162.5 bp (3.625 − 2.00). Second, the GBP/USD gap flipped sign on 17 September 2026. Before the Fed’s move the Bank of England’s 3.75% sat 12.5 bp above the Fed midpoint of 3.625%; afterwards it sat 12.5 bp below.

The gaps are a snapshot of official settings. They do not say which way a currency will go, and the sections below explain why.

Policy rates are not what forwards are priced off

Banks price forwards from money-market rates, not directly from the policy rate. The closest published overnight benchmarks are SOFR in dollars (published by the New York Fed, read here through FRED) and €STR in euros (published by the ECB).

On 19 October 2026, the latest date for which both were published when we fetched them, SOFR was 3.87% and €STR was 2.441%. Both sit close to their policy anchors: SOFR inside the Fed’s 3.75–4.00% range, and €STR just under the 2.50% deposit facility rate. The overnight gap was 142.9 bp (3.87 − 2.441), a little wider than the 137.5 bp policy gap.

For exchange rates we use the ECB’s euro foreign exchange reference rates. The ECB says these come from a daily concertation between central banks around 14:10 CET, are usually published around 16:00 CET, and are published for information purposes only. They are a single daily fixing, not the rate any particular trader dealt at. For 20 October 2026 they were EUR/USD 1.1215, EUR/GBP 0.84028, EUR/CHF 0.9237 and EUR/CAD 1.5758. The dollar crosses follow by division (our calculation): GBP/USD 1.1215 ÷ 0.84028 = 1.3347, USD/CHF 0.9237 ÷ 1.1215 = 0.8236 and USD/CAD 1.5758 ÷ 1.1215 = 1.4051.

A worked example: covered interest parity for EUR/USD

Covered interest parity says a forward exchange rate makes two routes equal: deposit dollars for a period, or convert to euros, deposit the euros, and contract today to convert back at the forward rate. If the routes paid different amounts, there would be a riskless profit. For a pair quoted as base/quote (EUR/USD: dollars per euro), the simple-interest form is F = S × (1 + i_quote × t) ÷ (1 + i_base × t), with t in years. Both SOFR and €STR use an actual/360 day count, so t is days ÷ 360.

Three months: from 20 October 2026 to 20 January 2027 is 92 days, so t = 92 ÷ 360 = 0.25556. The dollar leg is 1 + 0.0387 × 0.25556 = 1.009890. The euro leg is 1 + 0.02441 × 0.25556 = 1.006238. F = 1.1215 × 1.009890 ÷ 1.006238 = 1.1256, about 41 pips above spot.

One year: 365 days, so t = 365 ÷ 360 = 1.01389. The dollar leg is 1.039238, the euro leg 1.024749, and F = 1.1215 × 1.039238 ÷ 1.024749 = 1.1374, about 159 pips above spot.

The euro carries a forward premium because it is the lower-yielding currency. Holding euros earns less interest, and the higher forward price makes up the difference. The same arithmetic runs the other way when the base currency yields more. For USD/CHF, with no Swiss overnight rate on our tracker, using the SNB policy rate of 0.00% and the Fed midpoint as stand-ins gives a 3-month forward of 0.82363 × 1 ÷ (1 + 0.03875 × 0.25556) = 0.82363 ÷ 1.009903 = 0.8156, about 81 pips below spot.

These are approximations. Real forwards are priced off term money-market or overnight index swap rates for the exact period, which build in expected rate changes, and they include a cross-currency basis, a measurable deviation from parity that we do not have a primary source for. Dealer forward points will therefore differ from these figures.

Carry in plain terms

Carry is the interest a position earns or pays for each day it is held. Someone long EUR/USD is, in effect, holding euros and owing dollars, so on the overnight rates above they earn €STR and pay SOFR. On a notional of €1,000,000 that is about 1,000,000 × (0.03870 − 0.02441) ÷ 360 = €39.69 a day paid, before any dealer or broker markup (our calculation). The short side receives roughly the same amount. Retail brokers pass this through as a daily swap or rollover charge or credit, with their own spread added, so the posted figure differs by broker.

Parity explains why carry is not free money. The forward already moves against the higher-yielding currency by the rate gap. A carry position that is not hedged only comes out ahead if spot ends up better than that forward, and spot can move by more than a year of interest in a few days.

Why expectations move currencies more than the gap

Today’s gap is already known to everyone, so it is already in the price. What moves an exchange rate on a decision day is news about the path of rates, not their current level. If markets expect the Fed to raise again and it holds, the expected dollar advantage shrinks even though the policy gap is unchanged. That is why a currency can move sharply on a decision that was fully expected, if the guidance about later meetings changed, and why a statement, a press conference or the minutes can matter as much as the rate itself.

The term rates that forwards are priced from carry those expectations. A 1-year rate reflects the overnight rates the market expects over the next twelve months, so a change in the expected path changes the 1-year forward at once. Our overnight-rate example holds rates flat for the whole year, which is the main reason it is only an approximation.

The next scheduled tests are close together. The Fed announces on 28 October at the end of its 27–28 October meeting, the Bank of Canada also on 28 October, the ECB on 29 October and the Bank of England on 5 November. The SNB’s next monetary policy assessment is 10 December 2026. Any of them can change one leg of a gap; when two move by the same amount, as in September, the gap can stay put.

How to check the numbers yourself

Every figure here comes from a public series you can open.

• Fed range: FRED series DFEDTARU and DFEDTARL. Overnight dollar rate: FRED series SOFR.
• ECB deposit facility rate and €STR: the ECB Data Portal (deposit facility series FM.D.U2.EUR.4F.KR.DFR.LEV, and the euro short-term rate dataset), both linked in the sources.
• Bank Rate: the Bank of England Database, series IUDBEDR. Canada: the Bank of Canada Valet API, series V39079. Switzerland: the SNB data portal, cube snbgwdzid, row LZ.
• Exchange rates: the ECB’s euro foreign exchange reference rates page, daily or historical XML.
• Our central bank tracker at /central-banks shows each policy rate with its source and date, and /rates shows US Treasury yields and the effective fed funds rate.
• To redo the parity example, swap in the new spot and overnight rates and keep the same formula and day count.