CFA Level II Exam · Pricing and Valuation of Forward Commitments

Pricing and Valuation of Futures Contracts for CFA Level 2

Updated 7 October 2026 · Fact-checked

A futures price is the no-arbitrage price: spot grown at the risk-free rate, less the future value of benefits, plus the future value of costs. Futures are marked to market daily, so their value resets to zero after each settlement. In theory, futures and forward prices differ through interest-rate correlation; taxes, liquidity and credit risk can also matter.

Understand Pricing and Valuation of Futures Contracts

A futures contract is a standardised forward contract traded on an exchange. It has the same basic pricing logic. You can buy the asset today and carry it to expiry, or you can enter the futures contract. Both must cost the same, otherwise there is an arbitrage. This is the cost of carry idea: the futures price equals spot plus the net cost of holding the asset until delivery.

Carry has two sides. The cost side is the interest you give up by paying cash now, plus any storage cost. The benefit side is any cash flow the asset pays while you hold it, such as dividends, coupons, or a convenience yield. Benefits lower the futures price. Costs raise it.

The big difference from a forward is daily settlement. Each day the exchange clearing house moves cash between the long and short accounts based on the change in the futures price. This is marking to market. After settlement the contract is worth zero again, and the futures price is reset to the new settlement price. A forward has no such cash flows. Its value builds up until expiry, and it can be positive or negative in between.

Because of daily settlement, gains and losses on a futures contract are paid or received before expiry and can be reinvested or financed at the current rate. In theory, if interest rates are uncorrelated with futures prices, this makes no difference, and the futures price equals the forward price. If the correlation is positive, the long earns gains when rates are high and funds losses when rates are low. The long prefers futures, so the futures price is higher than the forward price. If the correlation is negative, the futures price is lower than the forward price. Other factors, such as taxes, liquidity and credit risk, can also cause the two prices to differ.

On the exam you are usually given a vignette with spot, rate, carry flows and settlement prices. Your job is to pick the right inputs, apply the formula, and not mix up futures value with forward value.

Key formulas to remember

Futures price, discrete compounding: F0(T) = S0 × (1 + r)^T − FV(benefits) + FV(costs); Equivalent form: F0(T) = (S0 − PV(benefits) + PV(costs)) × (1 + r)^T. These give the same result. Discount each cash flow only to today, or grow each to expiry, but do not do both. Use the same form consistently.
Futures price, continuous compounding with yield: F0(T) = S0 × e^((r − q) × T); r is the continuously compounded risk-free rate and q is the continuous yield on the asset, for example a dividend yield. Add a continuous storage cost rate to r if given.
Value of a futures contract after marking to market: Value after settlement = 0. Gain or loss for the day = (Ft − Ft−1) × multiplier × number of contracts for the long; The short gets the opposite sign. Ft is the settlement price.
Value of a forward contract at time t: Vt(T) = PV of (Ft(T) − F0(T)) = Ft(T) ÷ (1 + r)^(T − t) − F0(T) ÷ (1 + r)^(T − t); Long position. Not the same as futures value, which resets to zero daily.
Futures versus forward price: Correlation = 0: futures price = forward price. Positive correlation of futures prices with rates: futures price > forward price. Negative correlation: futures price < forward price; Applies to contracts with the same terms and expiry. Taxes, liquidity and credit risk are other reasons for differences.

How to solve Pricing and Valuation of Futures Contracts questions

Use this order for any futures pricing or valuation item in a vignette.

1Read the question and decide what is asked: a futures price at initiation, the gain or loss on a settlement day, the value of a forward, or a comparison of futures and forward prices.
2Pull the inputs from the vignette: spot price, risk-free rate, time to expiry in years, carry costs, benefits, multiplier and number of contracts.
3Check the compounding convention. Discrete rates use (1 + r)^T and continuous rates use e^(rT). Do not mix them.
4For pricing, adjust spot for benefits and costs, then compound to expiry. For continuous yield, use S0 × e^((r − q)T).
5For marking to market, take today's settlement price minus the previous settlement price, then multiply by the multiplier and the number of contracts. Flip the sign for a short.
6For a forward value, compare the current forward price with the original price and discount the difference from expiry back to today.
7For futures versus forward, identify the sign of the correlation between futures prices and interest rates, then name the direction of the difference.
8Sanity check: benefits should lower the price, costs raise it, and a positive interest rate should push the price above spot when there is no yield.

Quickest way: Carry-Sign Shortcut

When to use it: Use it when the options differ in size and direction and you need a fast price estimate or an arbitrage direction.

Start with spot. Add interest for the period. Subtract benefits grown to expiry. Add costs grown to expiry.
Compare with the quoted futures price. If quoted is higher, sell the futures, buy spot and borrow. If quoted is lower, buy the futures, short the asset and invest.
For a daily gain, subtract yesterday's settlement from today's and multiply. Ignore everything else.
For correlation questions, remember: positive means futures price above forward price, negative means below, zero means equal.

Common mistakes in Pricing and Valuation of Futures Contracts

Treating the value of a futures contract as the difference from the original futures price.
It is the correct approach for a forward, and the two contracts look alike.
Fix: Futures are reset to zero value after each daily settlement. Only the current day's change in settlement price is the gain or loss.
Adding dividends to spot instead of subtracting them.
Candidates focus on costs of carry and forget that benefits reduce the price.
Fix: Holding the asset earns the benefit, so the futures price is lower. Subtract the benefits and add the costs.
Mixing PV and FV forms for benefits or costs (for example, subtracting the PV and then also compounding the FV).
Candidates mix up PV and FV forms and count the same cash flow twice.
Fix: Use the PV form: discount each flow to today, subtract from spot, then compound the result to expiry. Or grow each flow to expiry and subtract. Do not do both.
Reversing the direction of the futures-forward price difference.
Candidates memorise the rule without the reasoning.
Fix: With positive correlation, the long's gains arrive when rates are high, which is good for the long. The long accepts a higher price, so futures > forward. Negative correlation reverses this.
Mixing continuous and discrete rates, or using months as years.
Vignettes state rates in different forms and expiries in months or days.
Fix: Convert time to years first, for example 6 months is 0.5. Use e^(rT) only when the rate is stated as continuously compounded.
Forgetting the contract multiplier or the number of contracts in the daily settlement.
The price change feels like the final answer.
Fix: Always multiply the price change by the multiplier and by the number of contracts, then apply the sign for long or short.

Worked examples

Example 1

Vignette: An equity index stands at 4,000. The continuously compounded risk-free rate is 4% and the index continuous dividend yield is 1.5%. A six-month index futures contract has a multiplier of 250. An investor holds 10 long contracts. The previous settlement price was 4,050.00 and today's settlement price is 4,062.00. Q1: What is the no-arbitrage futures price? Q2: What is the investor's gain for the day? Q3: What is the value of the contract position immediately after settlement?

Show the solution

Q1: F = S0 × e^((r − q) × T) = 4,000 × e^((0.04 − 0.015) × 0.5) = 4,000 × e^0.0125.
e^0.0125 ≈ 1.012578. So F ≈ 4,000 × 1.012578 = 4,050.31.
Note that the previous settlement price of 4,050.00 is a market price from the last trading day. It is not the model price, and it is not needed for Q1.
Q2: Price change = 4,062.00 − 4,050.00 = 12.00 index points.
Gain = 12 × 250 × 10 = 30,000 currency units. The investor is long, so this is a gain credited to the margin account.
Q3: After daily settlement the futures contract is marked to market and its value resets to zero.

Answer: Q1: about 4,050.31. Q2: a gain of 30,000. Q3: zero.

Example 2

Vignette: A commodity trades at 80 in the spot market. Storing it costs 3 per unit, payable in six months. The annual risk-free rate is 4%, compounded annually. A one-year futures contract trades at 88. The commodity pays no benefits. Q1: What is the no-arbitrage futures price? Q2: What trade exploits the quoted price? Q3: What is the arbitrage profit per unit at expiry?

Show the solution

Q1: PV of the storage cost = 3 ÷ (1.04)^0.5. Since √1.04 ≈ 1.019804, PV ≈ 2.9417.
F = (80 + 2.9417) × 1.04 = 82.9417 × 1.04 ≈ 86.26.
Check by future values: 80 × 1.04 = 83.20, and 3 × 1.04^0.5 ≈ 3.0594, so total 86.26. Same result.
Q2: The quoted price of 88 is above the fair price of 86.26, so the futures is overpriced. Sell the futures, buy the commodity at spot, and borrow to fund the purchase and storage.
Q3: At expiry deliver the commodity against the futures and receive 88. The cost, including financing, is 86.26. Profit = 88 − 86.26 ≈ 1.74 per unit.

Answer: Q1: about 86.26. Q2: sell the futures, buy spot and borrow. Q3: about 1.74 per unit, riskless.

Exam tips

Read the vignette for the compounding convention first. The rate form decides the formula.
Futures value after settlement is zero. If a question asks for the value of a futures contract at the end of the day, the answer is zero. If it asks for the day's gain, use the price change.
When two options differ only by sign, check long or short and whether benefits or costs are involved before choosing.
For futures versus forward, decide the correlation sign and apply the one rule. Do not overthink it.
Write the time to expiry in years beside the inputs before calculating, so you do not mix months and years.

Pricing and Valuation of Futures Contracts in other exams

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

Pricing and Valuation of Futures Contracts: frequently asked questions

What is the difference between forward and futures pricing?

Under no-arbitrage pricing both use the cost of carry. The difference is daily settlement. Futures gains and losses are paid each day, while a forward settles once at expiry. In theory the two prices are equal if interest rates are uncorrelated with futures prices, though taxes, liquidity and credit risk can also cause differences.

Why is the futures price higher than the forward price when rates are positively correlated with futures prices?

The long collects gains when rates are high, so it can reinvest them at a high rate. It pays losses when rates are low, so it funds them cheaply. This helps the long, so the futures price is higher than the forward price.

What is the value of a futures contract after marking to market?

It is zero. The clearing house settles the gain or loss in cash each day and resets the contract at the new settlement price. The day's gain is the price change times the multiplier times the number of contracts.

How do I calculate a futures price using cost of carry?

Start with spot, add the interest cost and any storage cost, and subtract benefits such as dividends. Compound the net amount to expiry. For a continuous yield, use S0 × e^((r − q)T).