FRM Exam Part I · Interest Rate Futures

Eurodollar and SOFR Futures: Pricing and Convexity Adjustment

Updated 11 October 2026 · Fact-checked

A Eurodollar or SOFR-type future is quoted as 100 minus an annualized rate. The contract price is 10,000 × [100 − 0.25 × (100 − Q)], where Q is the quote, so a one-basis-point move changes value by a fixed amount. A futures rate is higher than the matching forward rate because of the convexity adjustment: forward rate = futures rate − ½σ²T₁T₂.

Understand Eurodollar and Short-Term Rate Futures

A Eurodollar future is a contract on the interest rate for a three-month deposit of USD 1 million, starting on the contract's expiry date. The quote is not a price in the usual sense. It is 100 minus the annualized rate in percent. A quote of 96.50 means a rate of 3.50%. You gain when the quote rises (rates fall) if you are long.

The dollar value is set by a simple convention. A rate of 1% on USD 1 million for a quarter is USD 2,500. That means one basis point is worth USD 25. The contract price is therefore 10,000 × [100 − 0.25 × (100 − Q)], where Q is the quote. For Q = 96.50 this is USD 991,250. The mark-to-market cash flow each day is 25 × change in basis points.

LIBOR has been replaced by risk-free overnight rates. SOFR futures work in a similar way and are quoted as 100 minus a rate. The 3-month SOFR contract settles on the compounded SOFR over the reference quarter, and its tick value is also USD 25 per basis point. The 1-month SOFR contract has USD 3 million notional and is worth USD 25 per basis point (3,000,000 × 0.0001 × 1/12). A Eurodollar contract settles against a forward-looking LIBOR term rate fixed in advance, whereas SOFR is backward-looking and realized over the quarter.

A futures rate is not exactly a forward rate. Futures are settled daily. If rates rise, the long loses on the futures and has to fund that loss at higher rates. If rates fall, the long gains and reinvests at lower rates. This asymmetry works against the long, so the long requires a lower futures price, which means a higher futures rate. So the futures rate is above the forward rate. The gap is the convexity adjustment. It grows with the square of volatility and with the time to maturity, roughly with T₁ × T₂.

Under the Ho-Lee-type model used in the curriculum, forward rate = futures rate − ½σ²T₁T₂. T₁ is the time to the futures expiry. T₂ is the time to the end of the underlying rate period. σ is the annualized standard deviation of the short rate change. For short maturities the adjustment is tiny. For maturities of several years it matters when building a zero curve.

Key formulas to remember

Futures quote: Quote = 100 − annualized rate (in %); Rate = 100 − Quote. A higher quote means a lower rate.
Eurodollar contract value: Price = 10,000 × [100 − 0.25 × (100 − Quote)]; For USD 1 million, 3-month contract. The 0.25 is the accrual fraction.
Value of one basis point: USD 1,000,000 × 0.0001 × 0.25 = USD 25; Daily gain or loss for a long = 25 × change in quote in basis points.
Convexity adjustment: Forward rate = Futures rate − ½ × σ² × T₁ × T₂; Use decimals for rates, σ and years. Futures rate is the higher of the two.
Implied forward rate: Forward rate = (1/τ) × (Z(T₁)/Z(T₂) − 1); Simple rate over period τ from T₁ to T₂, using discount factors Z. Compare with the adjusted futures rate.

How to solve Eurodollar and Short-Term Rate Futures questions

Use this order for any Eurodollar or SOFR futures question. Decide first whether it asks for a rate, a dollar value, a gain or loss, or a forward rate.

1Read the quote and convert it to a rate: rate = 100 − quote, in percent.
2Identify the contract: 3-month, USD 1 million notional, USD 25 per basis point (3-month SOFR is the same). The 1-month SOFR contract has USD 3 million notional and is also worth USD 25 per basis point.
3For a dollar value, apply 10,000 × [100 − 0.25 × (100 − Q)]. For a gain or loss, count basis points moved and multiply by USD 25.
4Check the direction. Long gains when the quote rises. Short gains when the quote falls.
5If the question asks for a forward rate, convert the quote to a futures rate in decimals first.
6Compute the convexity adjustment: ½ × σ² × T₁ × T₂, with σ as a decimal. Subtract it from the futures rate.
7Convert back to percent if needed. Sanity check: the forward rate must be lower than the futures rate.

Quickest way: Basis-point shortcut

When to use it: Use it for gain, loss or P&L questions where you only need the change in value.

Find the change in quote and multiply by 100 to get basis points.
Multiply by USD 25 per contract (3-month Eurodollar, 3-month SOFR and 1-month SOFR all use USD 25 per basis point).
Flip the sign if you are short.
For convexity, compute σ² × T₁ × T₂ ÷ 2 directly in decimals, then convert to basis points by multiplying by 10,000.

Common mistakes in Eurodollar and Short-Term Rate Futures

Using the quote as the interest rate.
The quote looks like a price near 100, and students forget that rate = 100 − quote.
Fix: Always subtract from 100 before doing any rate work.
Forgetting the 0.25 accrual factor in the contract value.
Students treat the contract as USD 1 million times the annual rate.
Fix: The rate applies for three months, so multiply by 0.25. That gives USD 25 per basis point.
Adding the convexity adjustment to the futures rate.
The sign is easy to flip under time pressure.
Fix: Remember daily settlement works against the long, so the long needs a lower futures price, which means a higher futures rate. Forward = futures − adjustment.
Using σ in percent or time in months.
Inputs are quoted in mixed units.
Fix: Put σ as a decimal (0.012 for 1.2%) and T₁, T₂ in years before computing.
Getting the direction of profit wrong for a long position.
Students link long with rising rates.
Fix: Long a futures with a 100 − rate quote profits when rates fall and the quote rises.
Using T₂ − T₁ in the convexity formula.
Students confuse it with the accrual length.
Fix: The formula uses the product T₁ × T₂, both measured from today.

Worked examples

Example 1

You are long 10 three-month Eurodollar futures at 96.50. The settlement quote moves to 96.38. What is your gain or loss, and what is the implied rate at the new quote?

Show the solution

Change in quote = 96.38 − 96.50 = −0.12, which is −12 basis points.
Loss per contract = 12 × USD 25 = USD 300.
Loss on 10 contracts = 10 × USD 300 = USD 3,000.
Implied rate at the new quote = 100 − 96.38 = 3.62%.

Answer: A loss of USD 3,000; the implied rate is 3.62%.

Example 2

A Eurodollar futures contract expiring in 4 years is quoted at 95.00. The underlying rate covers the quarter from year 4 to year 4.25. The standard deviation of the short rate change is 1.2% per year. Estimate the forward rate, with the convexity adjustment.

Show the solution

Futures rate = 100 − 95.00 = 5.00%, or 0.0500.
T₁ = 4 and T₂ = 4.25.
Adjustment = ½ × (0.012)² × 4 × 4.25.
(0.012)² = 0.000144. Then 4 × 4.25 = 17.
½ × 0.000144 × 17 = 0.001224, or 0.1224%.
Forward rate = 5.00% − 0.1224% = 4.8776%.

Answer: The forward rate is about 4.88% (4.8776%), which is about 12 basis points below the futures rate.

Exam tips

Do the 100 − quote conversion first on every question. Many wrong answers come from skipping it.
Memorize USD 25 per basis point for 3-month contracts. It saves time on every P&L question.
Expect a question that asks which of the futures or forward rate is higher. The answer is futures, because of daily settlement.
Check units in the convexity formula: σ as a decimal, time in years. A result in the hundredths of a percent is typical for 2 to 5 years.
For SOFR versus Eurodollar, know the conceptual difference: SOFR is a backward-looking overnight rate compounded over the period, while the Eurodollar contract referenced a forward-looking term rate.

Practice questions from Interest Rate Futures

Eurodollar and Short-Term Rate Futures: frequently asked questions

How do you calculate the Eurodollar futures contract price?

Convert the quote to a rate with 100 minus the quote. Then apply 10,000 × [100 − 0.25 × (100 − Q)]. A quote of 96.50 gives USD 991,250.

What is the difference between a futures rate and a forward rate?

The futures rate comes from a contract settled daily, so gains and losses are reinvested or funded at changing rates. This pushes the futures rate above the forward rate. The difference is the convexity adjustment.

How big is the convexity adjustment?

It is ½σ²T₁T₂ in the standard curriculum model. It is small for short maturities and rises quickly as T₁ and T₂ increase or as volatility rises.

How do SOFR futures differ from Eurodollar futures?

Both are quoted as 100 minus a rate, and the 3-month contract is worth USD 25 per basis point. Eurodollar futures referenced a forward-looking USD LIBOR term rate. SOFR futures settle on SOFR realized over the reference period, a backward-looking, nearly risk-free rate.