CFA Level I Exam · Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Forward Contract Pricing Principles and No-Arbitrage

Updated 7 October 2026 · Fact-checked

The forward price is the delivery price that gives a forward contract zero value at initiation. No-arbitrage sets it equal to the spot price grown at the risk-free rate, adjusted for carry costs and benefits: F0 = S0 × (1 + r)^T for an asset with no cash flows. Later, the contract's value changes while the agreed price stays fixed.

Understand Forward Contract Pricing Principles

A forward contract is an agreement to buy or sell an asset at a fixed price on a future date. The fixed price is the forward price. Nothing is paid at the start, so the contract must have a value of zero for both sides when it is signed.

The pricing logic is no-arbitrage. You can replicate a forward by borrowing money today, buying the asset at the spot price, and holding it until delivery. If the forward price were different from the cost of doing that, someone could lock in a risk-free profit. Traders would exploit it until the gap closed. So the forward price equals the cost of buying and holding the asset until delivery.

Cost of carry is the net cost of holding the asset. Interest on the money tied up (the risk-free rate) pushes the forward price up. Storage costs push it up too. Benefits of holding, such as dividends, coupons or a convenience yield, pull it down. For an asset with no cash flows and no storage cost, the only carry is interest.

Do not confuse forward price with forward value. The forward price is the fixed delivery price written in the contract. It does not change after initiation. The value of the contract is what it is worth today, and it moves as the spot price and time change. At initiation, value is zero. At expiration, the long's value is ST − F0. In between, the long's value is the present value of the difference between the new forward price and the old one.

The model assumes no transaction costs, the ability to borrow and lend at the risk-free rate, and no counterparty default. Exam questions state these or ignore them.

Key formulas to remember

Forward price, no cash flows (discrete compounding): F0(T) = S0 × (1 + r)^T; r is the annual risk-free rate, T is in years. This is the future value of the spot price.
Forward price, continuous compounding: F0(T) = S0 × e^(rT); Use only if the question gives a continuously compounded rate.
Forward price with cash flows and costs: F0(T) = (S0 − PV of benefits + PV of costs) × (1 + r)^T; Benefits such as dividends or coupons lower the price. Storage costs raise it. Discount them to today first.
Forward price with a continuous yield: F0(T) = S0 × e^((r − δ)T); δ is the continuous dividend or benefit yield. Subtract a convenience yield in the same way, add a storage cost rate.
Value of a long forward during its life, no cash flows: Vt(T) = St − [F0(T) ÷ (1 + r)^(T − t)]; Only F0 is discounted, over the time remaining (T − t). The short's value is the negative of this.
Value of a long forward at expiration: VT(T) = ST − F0(T); The long gains when the spot price at expiry exceeds the agreed price.
General value of a long forward: Vt = PV of (new forward price − original forward price); Discount over the remaining life at the risk-free rate.

How to solve Forward Contract Pricing Principles questions

Use this method whether the question asks for a forward price, a contract value, or an arbitrage profit.

1Decide what is asked: the forward price at initiation, the value of the contract at a later date, or an arbitrage trade.
2List the inputs: spot price, risk-free rate, time to expiry, and any income or costs on the asset.
3Check the time units. Convert months to years and match the rate to the compounding stated.
4For price, adjust the spot first: subtract the present value of benefits, add the present value of costs, then compound at the risk-free rate to expiry.
5For value at a later date, find the current spot (adjusted for any remaining cash flows) and subtract the present value of the original forward price over the remaining time.
6If the market forward price differs from the fair price, find the arbitrage: if the market price is too high, sell the forward and buy the asset with borrowed money. If too low, buy the forward and short the asset, lending the proceeds.
7Sanity check the sign: the long's value is positive if the spot has risen relative to the original contract terms, and the short's value is the opposite.

Quickest way: Spot, carry, compare

When to use it: Use this for standard three-option MCQs where the algebra is short and you must answer in about 90 seconds.

Start from the spot price and ask: does the asset pay income? If yes, the forward is below the compounded spot. If no, the forward equals the compounded spot, which is above the spot itself.
Estimate the answer roughly. Compounding at a few percent for under a year changes the spot only slightly, which often eliminates one or two options.
Compute with the calculator only once. On the BA II Plus, enter (1 + r), press the [y^x] key, enter T, press [=], then multiply by S0. For example: 1.05 [y^x] 0.5 [=] then × 80. On the HP 12C, enter 1.05 [ENTER] 0.5 [yx], then 80 [×].
For value questions, remember a forward's value is not the forward price. If an option equals the new forward price itself, it is likely a trap.
Check the sign of your value answer against whether the spot rose or fell.

Common mistakes in Forward Contract Pricing Principles

Treating the forward price and the forward value as the same thing.
Both are called 'forward' and both appear in the same formulas.
Fix: Remember the price is a fixed number in the contract. The value starts at zero and changes. Ask yourself which one the question wants.
Forgetting to subtract the present value of dividends or coupons before compounding.
Students apply S0 × (1 + r)^T out of habit.
Fix: Read the stem for any income on the asset. Subtract its PV from the spot first, then compound.
Discounting the spot price too, or discounting F0 over the full original term, when valuing a contract.
The value formula has two terms, and it is easy to discount both or to grab the original term from the stem.
Fix: Write Vt = St − PV(F0) every time. Leave St undiscounted and discount only F0, over the remaining time T − t.
Using the wrong time period, such as full T instead of T − t.
The contract's original term is easy to grab from the stem.
Fix: Compute remaining time explicitly before discounting.
Assuming the forward price is a prediction of the future spot price.
The forward price looks like a forecast.
Fix: The forward price comes from arbitrage and carry, not from expectations. It can differ from the eventual spot price.
Reversing the arbitrage trade when the forward is mispriced.
Students mix up which side is overpriced.
Fix: If the market forward is above the fair price, sell the forward. If below, buy it. Then hedge with the asset the opposite way.

Worked examples

Example 1

A stock trades at $80 and pays no dividends. The annual risk-free rate is 5%. What is the no-arbitrage price of a forward contract expiring in 6 months? Options: A) $80.00 B) $81.98 C) $84.00

Show the solution

The asset has no cash flows, so F0 = S0 × (1 + r)^T.
T = 0.5, so F0 = 80 × (1.05)^0.5.
(1.05)^0.5 = 1.024695.
F0 = 80 × 1.024695 = 81.9756, which rounds to $81.98.
Option B matches the exact answer.

Answer: B) $81.98

Example 2

Three months ago you entered a long forward on a non-dividend stock at a forward price of $100 for a 1-year term. Now the stock trades at $104, and 9 months remain. The risk-free rate is 4% annually. What is the value of the long position? Options: A) $4.00 B) $6.90 C) $7.85

Show the solution

Use Vt = St − [F0 ÷ (1 + r)^(T − t)].
Remaining time is 0.75 years.
(1.04)^0.75 = 1.029852.
PV of F0 = 100 ÷ 1.029852 = 97.10.
Vt = 104 − 97.10 = 6.90.
Check: ln 1.04 = 0.039221; × 0.75 = 0.029416; e^0.029416 = 1.029852. So PV = 97.101 and V = 6.899, about $6.90.
Option A ($4.00) is 104 − 100, which ignores discounting. Option C ($7.85) is 104 − 100 ÷ 1.04, which discounts over a full year instead of 0.75 years.

Answer: B) $6.90 (positive for the long)

Exam tips

Read for the word 'value' versus 'price'. At initiation the value is zero, and exam writers use this as a trap option.
Underline any dividend, coupon or storage cost in the stem before you start calculating.
Because options run smallest to largest, use rough compounding to decide whether the answer is just above or just below the spot.
For arbitrage questions, decide first whether the market forward is above or below the fair price, then pick the matching trade.
Convert months to years carefully: 3 months is 0.25, 9 months is 0.75.

Practice questions from Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Forward Contract Pricing Principles in other exams

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

Forward Contract Pricing Principles: frequently asked questions

What is the difference between forward price and forward value?

The forward price is the fixed delivery price agreed at the start and it never changes. The forward value is what the contract is worth at a given time and it starts at zero. It then moves with the spot price and the time left.

What is the cost of carry in forward pricing?

It is the net cost of holding the underlying until delivery. Interest and storage costs add to it, while dividends, coupons and convenience yield reduce it. The forward price is the spot price adjusted for this net carry.

Why must a forward contract have zero value at initiation?

No cash changes hands at the start, and the forward price is set so neither side has an advantage. If the value were not zero, one side would be giving something up for nothing.

How do I find the arbitrage profit if a forward is mispriced?

Compare the market forward price to the fair one. If the market price is higher, sell the forward, buy the asset with borrowed money and deliver at expiry. The profit is the market price minus the fair price at expiry.