CFA Level I Exam · Pricing and Valuation of Futures Contracts

Pricing Interest Rate and FX Forwards and Futures

Updated 7 October 2026 · Fact-checked

Interest rate and currency forwards are priced by no-arbitrage. A forward rate agreement rate is the forward rate implied by two spot rates. A currency forward equals spot times the ratio of (1 + price-currency rate) to (1 + base-currency rate), which is covered interest rate parity. Match the periods and day-count first.

Understand Pricing Interest Rate and FX Forwards and Futures

A forward price is not a forecast. It is the price that leaves no risk-free profit. If the forward differed from the no-arbitrage level, you could borrow, lend and trade the contract to lock in a gain with no risk. Dealers do exactly this, so the forward price is pushed back to that level.

A forward rate agreement (FRA) fixes an interest rate today for a loan that starts at a future date. A 3x6 FRA covers a 90-day loan that begins in 90 days. The fair FRA rate is the forward rate implied by today's 90-day and 180-day rates. Borrowing for 180 days must cost the same as borrowing for 90 days and then rolling into the forward loan.

A currency forward works the same way. You can convert today at spot and invest at the foreign rate. Or you can invest at home and lock in a forward rate to convert later. With no arbitrage, both routes must end with the same amount. This is covered interest rate parity. The currency with the higher interest rate trades at a forward discount. The currency with the lower rate trades at a forward premium.

Interest rate futures are similar but are marked to market daily. Many are quoted as 100 minus the rate. A price of 96.00 implies a rate of 4.00%. The price moves opposite to the rate. A long position gains if rates fall. The CFA Level I focus is on FRAs and currency forwards, so know the futures quote and the basis point value.

One caution on conventions. Money market rates such as Libor-style rates are quoted as simple annualized rates, usually on a 360-day basis. Use simple interest with days/360 unless the question gives annual compounding.

Key formulas to remember

Covered interest rate parity (simple rates): F(P/B) = S(P/B) × [1 + i(P) × (days ÷ 360)] ÷ [1 + i(B) × (days ÷ 360)]; P is the price currency and B is the base currency in the quote P/B. Use the rates for the same term as the forward.
Covered interest rate parity (annual compounding): F(P/B) = S(P/B) × (1 + i(P))^T ÷ (1 + i(B))^T; Use only when the question gives annual rates with T in years.
Forward points: Forward points = F − S, usually quoted in pips (×10,000 for most pairs); Positive points mean the base currency (B in P/B) trades at a forward premium.
Forward rate implied by spot rates (FRA rate): FRA rate = [(1 + r(h) × h ÷ 360) ÷ (1 + r(g) × g ÷ 360) − 1] × 360 ÷ (h − g); g is days to FRA expiry and h is days to the end of the underlying loan. For a 3x6 FRA, g = 90 and h = 180.
FRA payoff at expiry (long, pays fixed): Payoff = NP × (L − FRA rate) × (days ÷ 360) ÷ [1 + L × (days ÷ 360)]; L is the actual market rate at expiry. The payoff is discounted because the FRA settles at the start of the loan period. The long gains if L is above the FRA rate.
FRA value before expiry (long): Value = NP × (new forward rate − original FRA rate) × [(h − g) ÷ 360] ÷ [1 + r(h) × h ÷ 360]; Here g is the days from today to FRA expiry and h is the days from today to the end of the loan, so h − g is the loan length. The rate difference is applied over the loan length (h − g). It is then discounted back to today using the current rate for h days.
Interest rate futures price: Futures price = 100 − annualized rate (in %); Basis point value of a 3-month contract = notional × 0.0001 × 90 ÷ 360.

How to solve Pricing Interest Rate and FX Forwards and Futures questions

Use this routine for any FRA or currency forward question. Most errors come from mismatched terms or an inverted quote.

1Identify the contract: FRA, interest rate future or currency forward. Note whether the question asks for a price, a value or a payoff.
2Write the day-count convention. Use days/360 with simple rates unless annual compounding is given.
3For a currency forward, identify the price currency and the base currency from the quote P/B. The quote tells you how many units of P buy one unit of B.
4Pick the right rates. For FRAs, use the rates for g days and h days. For currencies, use both rates for the forward's term.
5Plug into the formula. Put the price-currency growth factor in the numerator and the base-currency growth factor in the denominator.
6Sanity check with the rate rule. The higher-rate currency should be at a forward discount. For FRAs, an upward-sloping curve should give a forward rate above the spot rates.
7For valuation or payoff, find the new forward rate or actual rate and the difference from the contract rate. Multiply by notional and days/360, then discount.
8Check the sign and the answer's direction. Then eliminate options that match the common wrong versions, such as an inverted ratio.

Quickest way: Direction-first elimination for forward exchange rates

When to use it: Use for currency forward MCQs when you are short on time. With three options, direction alone often removes two.

Compare the two interest rates over the term. Decide which currency has the higher rate.
The higher-rate currency must be at a forward discount. So the quote P/B forward is above spot if P has the higher rate, and below spot if B has the higher rate.
Cross out options on the wrong side of spot. Often this leaves one option.
If two options remain, estimate the size: forward ≈ spot × (1 + rate difference × days/360). Pick the closer one.
On the BA II Plus, compute the two growth factors and divide them in one chain, then multiply by spot. Keep full decimals until the end.

Common mistakes in Pricing Interest Rate and FX Forwards and Futures

Inverting the ratio, so the base-currency rate sits in the numerator
Quotes like USD/EUR are read backwards, so the price and base currencies get swapped.
Fix: Read P/B as units of P per one unit of B. The price currency (P) rate goes on top. Check that the higher-rate currency ends up at a forward discount.
Using the wrong day-count or term, such as 180/365 or the full-year rate
Students memorize the annual formula and forget that money market rates are simple and annualized.
Fix: Use days/360 unless the question gives annual compounding. Scale each rate by the forward's term.
Using the 3-month rate and the 6-month rate directly as the 3x6 FRA rate
Students think the FRA rate is just the longer rate or an average.
Fix: Compute the implied forward rate from the growth factors: (1 + r6 × 180/360) ÷ (1 + r3 × 90/360), subtract 1, then annualize by 360/90.
Forgetting to discount the FRA payoff
The payoff looks like a simple interest difference times notional.
Fix: The FRA settles at the start of the loan, so divide by 1 + L × days/360, where L is the actual rate at expiry.
Treating the forward price as a prediction of the future spot rate
The forward seems like the market's view.
Fix: The forward reflects interest rate differences and no-arbitrage, not an expected spot rate. Covered interest parity holds without any view on the exchange rate.
Getting the sign of the FRA gain wrong
Students confuse the long FRA with a long bond.
Fix: The long FRA pays the fixed rate and receives the market rate. It gains when the market rate rises above the FRA rate. Interest rate futures priced as 100 − rate move the other way: a long futures position gains when rates fall.

Worked examples

Example 1

The 90-day rate is 5.00% and the 180-day rate is 5.40% (both simple, annualized, 360-day basis). What is the fair rate on a 3x6 FRA? A) 5.40% B) 5.73% C) 5.80%

Show the solution

A 3x6 FRA starts in g = 90 days and ends at h = 180 days. The loan lasts 90 days.
Growth factor to 180 days: 1 + 0.054 × 180/360 = 1.0270.
Growth factor to 90 days: 1 + 0.05 × 90/360 = 1.0125.
Ratio: 1.0270 ÷ 1.0125 = 1.014321.
Subtract 1: 0.014321 is the 90-day forward period rate.
Annualize: 0.014321 × 360/90 = 0.057284, about 5.73%.
Check: the curve slopes upward, so the forward rate should exceed 5.40%. A is too low. C is not supported by the data.

Answer: B) 5.73%

Example 2

The spot USD/EUR rate is 1.0800 (USD per 1 EUR). The 180-day USD rate is 4.50% and the 180-day EUR rate is 3.00%, both simple, annualized, 360-day basis. What is the 180-day forward rate? A) 1.0722 B) 1.0880 C) 1.1000

Show the solution

The quote is USD/EUR, so USD is the price currency and EUR is the base currency.
USD growth factor: 1 + 0.045 × 180/360 = 1.0225.
EUR growth factor: 1 + 0.03 × 180/360 = 1.0150.
Forward = 1.0800 × 1.0225 ÷ 1.0150 = 1.0800 × 1.007389 = 1.08798, about 1.0880.
Direction check: USD has the higher rate, so USD is at a forward discount and EUR is at a forward premium. A USD forward discount means more USD per EUR, so the USD/EUR forward must be above 1.0800. This rules out A.
A (1.0722) comes from inverting the ratio, which puts the forward below spot. C (1.1000) is too large: the rate difference of about 1.5% × 0.5 = 0.75% implies a forward only about 0.75% above spot, which is roughly 1.088.

Answer: B) 1.0880 USD per EUR (forward points of about +80 pips)

Exam tips

Questions are standalone and have three options. Direction logic (higher-rate currency at a forward discount) can often remove two options before you calculate.
Check the quote convention first. Many errors come from reading USD/EUR as EUR per USD.
Know FRA language: a 3x6 FRA means start in 3 months, end in 6 months, with a 90-day loan period. Check the day counts the question gives.
Expect the three trap options from an inverted ratio, a missing discount factor, and the wrong term. Compute fully, then match.
Keep four decimals for exchange rates and at least six decimals in intermediate growth factors. Options are listed from smallest to largest, so rounding matters.

Practice questions from Pricing and Valuation of Futures Contracts

Pricing Interest Rate and FX Forwards and Futures in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Pricing Interest Rate and FX Forwards and Futures: frequently asked questions

What is covered interest rate parity?

It is a no-arbitrage condition linking spot, forward and interest rates in two currencies. The forward rate equals spot times the ratio of the price-currency growth factor to the base-currency growth factor. If it fails, you can earn a risk-free profit by borrowing in one currency and lending in the other with a forward hedge.

How do you price a forward rate agreement?

Compute the forward rate implied by two spot rates for the period of the underlying loan. For a 3x6 FRA, divide the 180-day growth factor by the 90-day growth factor, subtract 1 and multiply by 360/90. That implied rate is the FRA rate that makes the initial value zero.

Does a higher interest rate mean a stronger forward currency?

No. The currency with the higher interest rate trades at a forward discount. The interest rate gain is offset by a lower forward value of that currency, so there is no arbitrage.

Why is the FRA payoff discounted?

The FRA settles at the start of the loan period, but the interest difference would normally be paid at the end. Discounting by 1 + L × days/360 converts the end-of-period amount to its value at settlement.