Futures Forwards and Swaps Mechanics
A long forward pays terminal spot minus the agreed delivery price. Futures settle gains and losses through margin. A plain interest-rate swap exchanges fixed and floating interest on a notional amount, usually without exchanging that principal.
The method at a glance
Illustrative borrower: matching notionals, dates and floating benchmark.
- Debt paid to lenderSOFR + 2%
- Swap: pay fixed, receive floating4% - SOFR
- Combined annual rate paid6%
The benchmark cancels. The loan spread, counterparty exposure and any basis mismatch remain.
| Concept | How it works | Watch for |
|---|---|---|
| Forward | Long payoff = quantity × (terminal spot - delivery price). | Using the terminal payoff as today’s contract value. |
| Futures | Track mark-to-market cash flows and the contract multiplier. | Treating margin as the purchase price of the asset. |
| Swap | Net the contractual fixed and floating legs over the accrual period. | Removing a loan spread that the swap does not hedge. |
01Forward
How it works: Long payoff = quantity × (terminal spot - delivery price).
Watch for: Using the terminal payoff as today’s contract value.
02Futures
How it works: Track mark-to-market cash flows and the contract multiplier.
Watch for: Treating margin as the purchase price of the asset.
03Swap
How it works: Net the contractual fixed and floating legs over the accrual period.
Watch for: Removing a loan spread that the swap does not hedge.
Original worked example
Turn floating-rate debt into fixed-rate debt
Debt costs SOFR + 2%. A matching swap pays fixed 4% and receives SOFR. Assume matching notionals, reset dates and accrual conventions.
- 1
Debt outflow: SOFR + 2%.
- 2
Swap net outflow: 4% - SOFR.
- 3
Combined outflow: SOFR + 2% + 4% - SOFR = 6%.
The benchmark rate cancels, leaving 6% before fees and other risks. The borrower still bears its loan obligations and swap counterparty exposure.
Illustrative assumptions and calculations for learning. Not observed market data or an official exam item.
Apply the method and check its limits
Before you start: Discount factors, contract multipliers and accrual fractions.
Price a forward, then value an existing contract
F₀ = S₀eʳᵀ; long value at t = Sₜ - Ke⁻ʳ⁽ᵀ⁻ᵗ⁾
These formulas assume a non-income-paying asset, constant continuously compounded financing and frictionless carry. With spot 100, annual financing 5% and one year, the fair delivery price is approximately 105.127. A new contract struck there has zero initial value under the model. Its agreed K remains fixed while the value of the existing contract changes.
Turn rates into actual swap payments
Net fixed-payer payment = notional × (fixed rate - floating rate) × accrual fraction
On 10 million notional, fixed 4%, floating 3% and a quarter-year accrual, the fixed payer pays net 25,000 for that period. If floating rises to 5%, the same party receives net 25,000. The notional is a calculation base, not normally principal exchanged in a plain single-currency interest-rate swap.
Fair delivery price is different from value after inception
For a non-income-paying asset with no storage costs and continuously compounded financing rate r, the idealized forward price is S₀e^(rT). Existing contracts can gain or lose value as the spot price, rates or remaining maturity change. Dividends, storage, convenience yield and funding constraints alter the simple carry relationship.
Work through the topic
Write the contract’s cash flows, distinguish a new fair price from an existing contract’s value, and reconcile a hedge with the borrowing or purchase it is intended to offset.
Separate the forward delivery price from contract value
For a non-income-paying asset under a simple no-arbitrage model with continuous financing rate r, the fair forward delivery price is F₀ = S₀eʳᵀ. The rate and time convention must match. This relation assumes the relevant financing and trading arrangements are available and ignores complications such as transaction costs, storage constraints or convenience benefits. A commodity or income-paying asset can require a different carry adjustment.
Take an original one-year example with spot 100 and a continuously compounded financing rate of 5%. The fair delivery price is approximately 105.1271. A newly entered forward at that delivery price can have zero initial value even though its quoted delivery price is above zero. The price is the amount agreed for future exchange; value is the current worth of the contractual rights and obligations.
Half a year later, suppose spot is 108 and the same financing rate applies. The old long forward with delivery price 105.1271 has value 108 - 105.1271e⁻⁰·⁰²⁵, approximately 5.4685 per unit, under the same model. A new half-year forward would instead have delivery price 108e⁰·⁰²⁵, approximately 110.7340. Subtracting the old and new delivery prices without discounting would confuse a future cash difference with its present value.
| Date and object | Amount per unit | Interpretation |
|---|---|---|
| Initial one-year forward price | 105.1271 | Agreed future delivery price for a zero-value new contract |
| New forward price after six months | 110.7340 | Fair price for a newly entered remaining half-year contract |
| Existing long contract value then | 5.4685 | Current value of receiving the asset for the old delivery price |
Original forward example: price and value are different quantities
- Initial one-year forward price
- Amount per unit: 105.1271
- Interpretation: Agreed future delivery price for a zero-value new contract
- New forward price after six months
- Amount per unit: 110.7340
- Interpretation: Fair price for a newly entered remaining half-year contract
- Existing long contract value then
- Amount per unit: 5.4685
- Interpretation: Current value of receiving the asset for the old delivery price
Track futures settlement and the hedge direction
A long futures position gains when the quoted futures price rises and loses when it falls, subject to the contract’s quotation convention. For contracts representing physical units, a one-day gain is the number of contracts times the multiplier times the price increase. Some contracts quote prices through transformed rates or index conventions, so identify the quoted variable before translating an economic concern into a trade direction.
Suppose a manufacturer buys 25 contracts, each covering 1,000 units. A price rise of 0.40 per unit produces 25 × 1,000 × 0.40 = 10,000 of futures gain. A fall of the same size creates a loss and may require funding. If the manufacturer’s physical purchase occurs later, the eventual cheaper purchase does not itself provide cash for today’s margin call. The hedge must be evaluated in both value and cash terms.
Daily settlement means futures and forwards do not always have identical values or cash paths, even when their terminal economic exposures look similar. Financing and the interaction between rates and contract prices can matter. For the FRM mechanics task, first reconcile the position direction, multiplier and settlement dates. Then identify residual basis and funding exposures instead of assuming the hedge is complete because the terminal signs offset.
Reconcile the debt and both swap legs
Assume a firm borrows 10 million at a floating benchmark plus 2% and enters a swap paying fixed 4% and receiving that same benchmark. Use matching notionals, accrual periods and payment dates. The benchmark payments cancel in the simplified combined position, leaving 6% annualized interest before fees and other contractual effects. The loan is still outstanding; the swap changes its rate exposure rather than extinguishing the debt.
For a quarter with an accrual fraction of 0.25 and a realized benchmark of 3%, loan interest is 10 million × 5% × 0.25 = 125,000. The swap pays 100,000 fixed and receives 75,000 floating, a net payment of 25,000. Combined interest is 150,000. If the benchmark is 5% instead, loan interest becomes 175,000 and the swap receives a net 25,000, again leaving 150,000 under the matching assumptions.
A mismatch in benchmark, reset dates, day-count conventions or notional prevents exact cancellation. If the loan’s credit spread changes, the plain swap does not automatically offset that change either. Check collateral and counterparty exposures separately. The calculation demonstrates a specified cash-flow relationship; it is not proof that every floating-rate liability can be converted into a fully fixed all-in cost by any pay-fixed swap.
| Benchmark | Loan and net swap payment | Combined interest |
|---|---|---|
| 3% | 125,000 loan + 25,000 swap | 150,000 |
| 5% | 175,000 loan - 25,000 swap receipt | 150,000 |
| Different benchmark on the swap | The benchmark terms no longer cancel | Residual basis exposure remains |
Quarterly cash flows for the original 10 million hedge
- 3%
- Loan and net swap payment: 125,000 loan + 25,000 swap
- Combined interest: 150,000
- 5%
- Loan and net swap payment: 175,000 loan - 25,000 swap receipt
- Combined interest: 150,000
- Different benchmark on the swap
- Loan and net swap payment: The benchmark terms no longer cancel
- Combined interest: Residual basis exposure remains
Why can a forward have zero value but a nonzero delivery price?
At inception, the present values of what each side gives and receives can be equal. The agreed delivery price is still the amount exchanged at maturity. After market conditions change, the old delivery price stays fixed while the contract’s current value changes.
Which swap side offsets rising floating borrowing costs?
In the matching simplified structure, paying fixed and receiving the same floating benchmark offsets the benchmark component of floating-rate debt. Write all three legs with signs to verify the result. A receiving-fixed swap would create a different combined exposure, and unmatched spreads or conventions can remain.
Try a changed assumption
Floating debt costs SOFR + 2%, but the swap receives a different benchmark. Is the combined cost guaranteed to be 6%?
Show answer and reasoning
No. The two floating legs may not cancel. Their difference creates basis risk, even if notionals and payment dates match.
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Which side of a swap hedges floating-rate debt?
Pay fixed and receive the matching floating benchmark. Floating-rate assets generally require the opposite direction to create fixed receipts. Always write both cash-flow streams first.
Sources and scope
Links checked 2026-10-10. GARP establishes exam scope; the technical references support the methods identified below. These are selected study notes and original examples, not complete curriculum coverage or official exam questions.
- GARP FRM study materials and 2026 learning objectives
Exam-domain scope and the official route to the annual learning objectives. This page does not certify coverage of every reading.
- MIT OpenCourseWare: forward and futures contracts
Contract payoffs, no-arbitrage pricing and the distinction between forwards and futures.
- CME: pricing and hedging SOFR interest-rate swaps
Fixed and floating payment legs, notional, dates and accrual conventions.
Prepared by MiloPrep editorial team. MiloPrep is independent of GARP. References do not imply endorsement or independent review of these notes.