CFA Level I subject

Derivatives practice questions

Derivatives questions cover forwards, futures, swaps, options, replication logic, payoffs, and risk-transfer mechanics. This section currently includes 80 public practice questions across 20 topic modules, with explanations, formulas, traps, and key takeaways.

Indicative public exam weight: 5-8%. Start with a topic guide when you need focused review, or use adaptive mode for mixed practice and due reviews.

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Binomial Model

1 public question with explanations, formulas, and exam traps.

Credit Derivatives

1 public question with explanations, formulas, and exam traps.

Derivative Instrument and Market Features

7 public questions with explanations, formulas, and exam traps.

Forward Pricing

1 public question with explanations, formulas, and exam traps.

Forward Valuation

1 public question with explanations, formulas, and exam traps.

Futures and Swaps

1 public question with explanations, formulas, and exam traps.

Option Payoffs and Profits

1 public question with explanations, formulas, and exam traps.

Option Valuation Concepts

2 public questions with explanations, formulas, and exam traps.

Pricing and Valuation of Futures Contracts

11 public questions with explanations, formulas, and exam traps.

Put-Call Forward Parity

1 public question with explanations, formulas, and exam traps.

Put-Call Parity

1 public question with explanations, formulas, and exam traps.

Swaps

1 public question with explanations, formulas, and exam traps.

Forward Commitment and Contingent Claim Features and Instruments

8 public questions with explanations, formulas, and exam traps.

Derivative Benefits, Risks, and Issuer and Investor Uses

6 public questions with explanations, formulas, and exam traps.

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

7 public questions with explanations, formulas, and exam traps.

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

6 public questions with explanations, formulas, and exam traps.

Valuing a Derivative Using a One-Period Binomial Model

4 public questions with explanations, formulas, and exam traps.

Pricing and Valuation of Interest Rates and Other Swaps

7 public questions with explanations, formulas, and exam traps.

Pricing and Valuation of Options

8 public questions with explanations, formulas, and exam traps.

Option Replication Using Put-Call Parity

5 public questions with explanations, formulas, and exam traps.

Moderate

Derivatives

Binomial Model

A stock price is 50. In one period it will move up by 20% or down by 15%. The risk-free rate per period is 4%. A one-period European call has exercise price 52. The call value is closest to:

Moderate

Derivatives

Credit Derivatives

A portfolio manager buys credit protection on a corporate bond through a derivative contract. The manager pays periodic premiums and receives compensation if a defined credit event occurs. The position is most accurately described as:

Moderate

Derivatives

Derivative Instrument and Market Features

A corporate treasurer enters a customized bilateral contract with a bank to exchange fixed payments for floating payments for five years. The contract is most accurately classified as:

Moderate

Derivatives

Forward Pricing

A non-dividend-paying asset sells for 80. The annual risk-free rate is 5% with annual compounding, and a one-year forward contract is initiated today. The no-arbitrage forward price is closest to:

Moderate

Derivatives

Forward Valuation

Six months remain on a forward contract on a non-income-producing asset. The original forward price is 103.50, the current spot price is 108.00, and the six-month risk-free rate is 2.0%. The value of the forward contract to the long is closest to:

Moderate

Derivatives

Futures and Swaps

A futures contract and an otherwise comparable forward contract have the same underlying and maturity. Futures are most likely to differ from forwards because futures:

Moderate

Derivatives

Option Payoffs and Profits

A trader buys a put with exercise price USD55 for a premium of USD4. At expiration, the underlying price is USD48. The put payoff and profit per share are closest to:

Moderate

Derivatives

Option Valuation Concepts

A European call with exercise price 100 trades for 8 when the underlying is 104. The option's exercise value and time value are, respectively:

Moderate

Derivatives

Option Valuation Concepts

Holding other inputs constant, which change most likely increases the value of both a European call and a European put on a non-dividend-paying stock?

Easy

Derivatives

Pricing and Valuation of Futures Contracts

Immediately after a futures contract has been marked to market at the daily settlement price, the value of the contract is most likely:

Easy

Derivatives

Pricing and Valuation of Futures Contracts

A three-month interest rate futures contract on the market reference rate is quoted at a price of 97.20. The annualized futures market reference rate implied by this quote is closest to:

Moderate

Derivatives

Pricing and Valuation of Futures Contracts

Lucia Fernandez buys two gold futures contracts at a price of USD 1,950.00 per ounce; each contract covers 100 ounces. The initial margin is USD 8,000 per contract and the maintenance margin is USD 7,200 per contract. At the end of the first trading day, the settlement price is USD 1,940.00. The variation margin Fernandez must deposit is closest to:

Moderate

Derivatives

Pricing and Valuation of Futures Contracts

A futures contract and an otherwise identical forward contract are written on the same underlying asset. The futures price most likely exceeds the forward price when the underlying's futures price is:

Moderate

Derivatives

Pricing and Valuation of Futures Contracts

As a commodity futures contract approaches its expiration date, the difference between the futures price and the spot price of the underlying most likely:

Very Difficult

Derivatives

Pricing and Valuation of Futures Contracts

Kwame Mensah sells four crude oil futures contracts at USD 72.50 per barrel; each contract covers 1,000 barrels. The initial margin is USD 5,500 per contract and the maintenance margin is USD 5,000 per contract. Settlement prices are USD 72.95 at the end of Day 1 and USD 73.30 at the end of Day 2. Mensah makes no withdrawals or deposits before any required margin call. The variation margin Mensah must deposit at the end of Day 2 is closest to:

Very Difficult

Derivatives

Pricing and Valuation of Futures Contracts

Ingrid Larsen is long one three-month interest rate futures contract with a notional principal of USD 1,000,000. The contract is quoted at 97.50 when she buys it, implying an annualized market reference rate of 2.50%. At the next daily settlement, the quoted price is 97.26. Using a 90/360 period adjustment, the mark-to-market settlement on Larsen's position for that day is closest to:

Moderate

Derivatives

Put-Call Forward Parity

A one-year forward price on an asset is 106, the exercise price on European options is 100, and the annual risk-free rate is 3%. Under put-call-forward parity, c - p is closest to:

Moderate

Derivatives

Put-Call Parity

A non-dividend-paying stock trades at 52. A one-year European call with exercise price 50 trades at 6. The annual risk-free rate is 5%. The no-arbitrage European put price is closest to:

Moderate

Derivatives

Swaps

At initiation, an interest rate swap's fixed rate is set so the contract has zero value to both parties. Six months later, market swap fixed rates fall below the original fixed rate. For the fixed-rate payer, the original swap most likely has:

Easy

Derivatives

Derivative Instrument and Market Features

A financial instrument is best described as a derivative if it:

Easy

Derivatives

Derivative Instrument and Market Features

A derivative contract is least likely to permit physical delivery of its underlying when the underlying is:

Moderate

Derivatives

Derivative Instrument and Market Features

A food processing company needs to hedge the purchase of 34,600 bushels of corn for delivery to a specific plant on a date that falls between exchange contract expirations. Relative to hedging with exchange-traded futures, hedging with an over-the-counter forward most likely provides:

Moderate

Derivatives

Derivative Instrument and Market Features

In a centrally cleared derivatives market, the central counterparty (CCP) most likely reduces counterparty credit risk by:

Difficult

Derivatives

Derivative Instrument and Market Features

A derivatives dealer has historically transacted interest rate swaps bilaterally with dozens of counterparties, exchanging collateral under individually negotiated agreements. New regulation now requires all standardized swaps to be centrally cleared. The most likely effect of this change on the dealer is that its:

Moderate

Derivatives

Derivative Instrument and Market Features

A trader buys three equity index futures contracts at a price of 4,250.00. The contract multiplier is USD 50 per index point. At the end of that trading day, the daily settlement price is 4,238.00. As a result of the daily mark to market, the change in the trader's margin account balance is closest to:

Easy

Derivatives

Forward Commitment and Contingent Claim Features and Instruments

A contingent claim differs from a forward commitment most likely in that a contingent claim:

Moderate

Derivatives

Forward Commitment and Contingent Claim Features and Instruments

An interest rate swap in which one party pays a fixed rate and receives a floating rate on several future settlement dates is most accurately described as economically equivalent to:

Moderate

Derivatives

Forward Commitment and Contingent Claim Features and Instruments

A European put option with an exercise price of USD 75 is trading while its underlying stock trades at USD 82. The option is best described as:

Moderate

Derivatives

Forward Commitment and Contingent Claim Features and Instruments

Holding the underlying price, volatility, and other pricing inputs constant, as a European option approaches its expiration date, the option's time value most likely:

Moderate

Derivatives

Forward Commitment and Contingent Claim Features and Instruments

An investor with no existing exposure to a corporate issuer sells credit protection on that issuer using a single-name credit default swap. The investor's position is best described as:

Difficult

Derivatives

Forward Commitment and Contingent Claim Features and Instruments

A company pays a floating market reference rate plus a spread on USD 200 million of debt that resets quarterly. The treasurer wants to lock in a known interest cost for the next five years, insists on zero initial cost, and is willing to give up any benefit from falling rates. The most appropriate instrument is:

Moderate

Derivatives

Forward Commitment and Contingent Claim Features and Instruments

A trader writes a call option with an exercise price of USD 45 and receives a premium of USD 3.00 per share. At expiration, the underlying stock trades at USD 51. The writer's profit per share is closest to:

Very Difficult

Derivatives

Forward Commitment and Contingent Claim Features and Instruments

An investor buys 100 shares of a stock at USD 62.00 per share and simultaneously buys one put option covering 100 shares with an exercise price of USD 60.00, paying a premium of USD 2.50 per share. At the option's expiration, the stock trades at USD 54.00. The investor's total profit per share on the combined position is closest to:

Easy

Derivatives

Derivative Benefits, Risks, and Issuer and Investor Uses

The information discovery benefit of derivative markets is best illustrated by market participants:

Moderate

Derivatives

Derivative Benefits, Risks, and Issuer and Investor Uses

A portfolio manager wants to reduce a diversified equity portfolio's market exposure for three months and restore it afterward. Compared with selling the portfolio's shares and later repurchasing them, selling equity index futures most likely offers:

Difficult

Derivatives

Derivative Benefits, Risks, and Issuer and Investor Uses

Because jet fuel futures with a suitable expiration are unavailable, an airline hedges an anticipated jet fuel purchase by buying heating oil futures. When the hedge is closed, jet fuel prices have risen 9% while the heating oil futures price has risen only 5%, leaving the airline with a materially larger net fuel cost than planned. The shortfall is best attributed to:

Moderate

Derivatives

Derivative Benefits, Risks, and Issuer and Investor Uses

An investor holds a customized, long-dated over-the-counter option purchased from a dealer. When the investor seeks to exit the position early, the original dealer is the only party willing to quote a price, and its bid is well below the option's estimated model value. The investor's difficulty is best described as:

Difficult

Derivatives

Derivative Benefits, Risks, and Issuer and Investor Uses

A U.S. exporter forecasts EUR 50 million of sales receipts in six months and sells EUR 50 million forward against the U.S. dollar. Convinced that the euro will depreciate more than the forward rate implies, the treasurer then increases the total forward sale to EUR 90 million. The additional EUR 40 million forward position is best described as:

Easy

Derivatives

Derivative Benefits, Risks, and Issuer and Investor Uses

A primary benefit of derivative markets to the financial system is that they most likely allow:

Easy

Derivatives

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

Two portfolios are certain to produce identical cash flows on the same future dates in every possible state of the world, yet they currently trade at different prices. According to the law of one price, this situation is best described as:

Moderate

Derivatives

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

An investor buys a non-dividend-paying asset at the spot price and simultaneously sells a forward contract on that asset at the no-arbitrage forward price, holding both positions until the forward expires. The return earned on this combined position is most likely:

Moderate

Derivatives

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

The spot price of a storable commodity currently exceeds its forward price for delivery in one year, and the risk-free rate is positive. This relationship is most likely explained by:

Moderate

Derivatives

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

The spot price of a storable industrial metal is USD 40.00 per unit. Storage and insurance costs of USD 2.00 per unit are payable at the end of one year, the annual risk-free rate is 5.0% with annual compounding, and holding the metal provides no convenience yield or other benefits. The no-arbitrage price of a one-year forward contract on the metal is closest to:

Moderate

Derivatives

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

A stock trades at USD 75.00 and will pay a single dividend of USD 1.50 immediately before the expiration of a one-year forward contract on the stock. The annual risk-free rate is 4.0% with annual compounding. The no-arbitrage one-year forward price is closest to:

Difficult

Derivatives

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

A metals analyst prices a one-year forward contract on a commodity with a spot price of USD 1,200.00 per unit. The annual risk-free rate is 3.0% with annual compounding. Storage costs with a value of USD 24.00 as of expiration will be incurred, and the convenience yield of holding the physical commodity has a value of USD 10.00 as of expiration. The no-arbitrage one-year forward price is closest to:

Difficult

Derivatives

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

A non-dividend-paying asset trades at a spot price of USD 60.00, and the annual risk-free rate is 6.0% with annual compounding. A dealer quotes a one-year forward price of USD 65.00 on the asset. An arbitrageur borrows the full purchase price at the risk-free rate, buys the asset at spot, and sells the forward at the quoted price, holding the position to expiration. The arbitrage profit at expiration, per unit of the asset, is closest to:

Easy

Derivatives

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

A forward contract is initiated today at the no-arbitrage forward price, and no money changes hands. At initiation, the value of the contract to the long is most likely:

Moderate

Derivatives

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

A company plans to borrow for six months beginning in three months and takes a long position in a forward rate agreement (FRA) to hedge the exposure. At the FRA's expiration in three months, the market reference rate sets above the FRA fixed rate. The company most likely:

Moderate

Derivatives

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

The spot exchange rate is USD 1.1000 per EUR 1. The one-year risk-free rate is 6.0% in USD and 1.0% in EUR, both with annual compounding. The no-arbitrage one-year forward exchange rate, in USD per EUR, is closest to:

Moderate

Derivatives

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

A forward contract on a non-income-producing asset was initiated at a forward price of USD 92.00. With three months remaining to expiration, the asset's spot price is USD 87.50, and the annual risk-free rate is 4.0% with annual compounding. The value of the contract to the short is closest to:

Difficult

Derivatives

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

Nine months ago, an investor took a long position in a one-year forward contract on a dividend-paying stock at a forward price of USD 118.00. The stock now trades at USD 121.00 and will pay a single dividend of USD 1.00 immediately before the contract expires in three months. The annual risk-free rate is 5.0% with annual compounding. The current value of the forward contract to the long is closest to:

Difficult

Derivatives

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

An equity index stands at 3,600.00. Index constituents are expected to pay dividends with a value of 36.00 index points as of the expiration of a six-month forward contract on the index. The annual risk-free rate is 4.0% with annual compounding. The no-arbitrage six-month forward price of the index is closest to:

Easy

Derivatives

Pricing and Valuation of Futures Contracts

One investor holds a long forward contract and another holds a long futures contract on the same underlying with the same expiration. The price of the underlying rises steadily over the life of both contracts. The difference in how the two investors' gains are received is best described as follows:

Moderate

Derivatives

Pricing and Valuation of Futures Contracts

Futures prices on an asset are strongly negatively correlated with interest rates. Relative to the price of an otherwise identical forward contract on that asset, the futures price is most likely:

Difficult

Derivatives

Pricing and Valuation of Futures Contracts

Priya Raman sells four equity index futures contracts at a price of 1,850.00; the contract multiplier is USD 25 per index point. The settlement price is 1,861.50 at the end of Day 1 and 1,842.75 at the end of Day 2. The cumulative mark-to-market cash flow on Raman's position over the two days is closest to:

Difficult

Derivatives

Pricing and Valuation of Futures Contracts

Tomas Novak buys two silver futures contracts at USD 24.80 per ounce; each contract covers 5,000 ounces. The initial margin is USD 9,900 per contract and the maintenance margin is USD 9,000 per contract, and Novak deposits exactly the initial margin. The settlement price below which Novak will receive a margin call is closest to:

Moderate

Derivatives

Valuing a Derivative Using a One-Period Binomial Model

In a one-period binomial model, the weights applied to the up-move and down-move payoffs when valuing an option are most accurately described as:

Easy

Derivatives

Valuing a Derivative Using a One-Period Binomial Model

In a one-period binomial model, a stock's price can move up by a factor of 1.30 or down by a factor of 0.90 over the period, and the risk-free rate for the period is 4.0%. The risk-neutral probability of an up move is closest to:

Moderate

Derivatives

Valuing a Derivative Using a One-Period Binomial Model

A stock trades at USD 100.00 and in one period will move to either USD 115.00 or USD 90.00. A one-period European call option on the stock has an exercise price of USD 100.00. The hedge ratio, the number of shares of stock to hold for each call option written so that the hedged portfolio is riskless, is closest to:

Very Difficult

Derivatives

Valuing a Derivative Using a One-Period Binomial Model

A stock trades at USD 80.00. Over one period, its price will either rise by 25% or fall by 20%. The risk-free rate for the period is 5.0%. A one-period European put option on the stock has an exercise price of USD 85.00. The value of the put option today is closest to:

Easy

Derivatives

Pricing and Valuation of Interest Rates and Other Swaps

An interest rate swap in which one party pays a fixed rate and receives a floating rate on each settlement date is most accurately described as economically equivalent to:

Moderate

Derivatives

Pricing and Valuation of Interest Rates and Other Swaps

At the initiation of a fixed-for-floating interest rate swap, the swap's fixed rate is most accurately described as the rate that:

Moderate

Derivatives

Pricing and Valuation of Interest Rates and Other Swaps

A two-year pay-fixed interest rate swap with semiannual settlements is compared with the series of forward rate agreements implicit in the swap. If the term structure is upward sloping, which statement about the implicit forward rate agreements at swap initiation is most accurate?

Easy

Derivatives

Pricing and Valuation of Interest Rates and Other Swaps

A company has issued five-year floating-rate debt on which interest resets semiannually. The treasurer wants to convert the exposure into a known, fixed interest expense for the remaining life of the debt. The most appropriate action is to enter an interest rate swap in which the company:

Moderate

Derivatives

Pricing and Valuation of Interest Rates and Other Swaps

A company is the fixed-rate payer on an interest rate swap with a notional principal of USD 20,000,000 and semiannual net settlement on a 180/360 day-count basis. The swap fixed rate is 3.60%, and the market reference rate set at the beginning of the current period is 3.10%. The net payment made by the fixed-rate payer at the end of the period is closest to:

Difficult

Derivatives

Pricing and Valuation of Interest Rates and Other Swaps

One year ago, an investor entered a three-year receive-fixed interest rate swap with annual settlements at a fixed rate of 4.00% on a notional principal of USD 10,000,000. Today, immediately after the first settlement, the market swap rate for a new two-year swap is 3.40%, and the present value factors for payments due in one and two years are 0.97 and 0.93, respectively. The value of the swap to the fixed-rate receiver is closest to:

Difficult

Derivatives

Pricing and Valuation of Interest Rates and Other Swaps

An asset manager enters an equity swap on a notional principal of USD 5,000,000, agreeing to receive the price return of an equity index and pay a fixed rate of 2.80% per year, with quarterly settlements on a 90/360 day-count basis. Over the first quarter, the index rises from 1,500.00 to 1,545.00. The net amount the manager receives at the first settlement is closest to:

Easy

Derivatives

Pricing and Valuation of Options

Holding all other factors constant, an increase in the risk-free interest rate most likely results in:

Moderate

Derivatives

Pricing and Valuation of Options

Prior to expiration, the maximum possible value of a European put option is most accurately described as:

Moderate

Derivatives

Pricing and Valuation of Options

For options written on a stock that pays no dividends, early exercise is most likely to be rational for the holder of:

Easy

Derivatives

Pricing and Valuation of Options

As an option's expiration date approaches, with all other factors unchanged, the time value component of the option's price most likely:

Moderate

Derivatives

Pricing and Valuation of Options

A European put option with an exercise price of USD 75.00 trades at a price of USD 6.20 when the underlying stock trades at USD 71.00. The put's exercise value and time value are, respectively, closest to:

Moderate

Derivatives

Pricing and Valuation of Options

A non-dividend-paying stock trades at USD 64.00. A one-year European call option on the stock has an exercise price of USD 60.00, and the annual risk-free rate is 4.00%. The lower bound on the call option's value is closest to:

Difficult

Derivatives

Pricing and Valuation of Options

A non-dividend-paying stock trades at USD 45.00. A six-month European put option on the stock has an exercise price of USD 50.00, and the annual risk-free rate is 5.00%. The lower bound on the put option's value is closest to:

Difficult

Derivatives

Pricing and Valuation of Options

An investor writes a European call option with an exercise price of USD 90.00 and receives a premium of USD 5.60 per share. At expiration, the underlying stock trades at USD 97.00. Ignoring transaction costs, the writer's profit per share and the breakeven underlying price at expiration are, respectively, closest to:

Easy

Derivatives

Option Replication Using Put-Call Parity

An investor holds a protective put consisting of one share of a non-dividend-paying stock and one European put option on that share. At the options' expiration, the payoff of this position is identical to the payoff of holding:

Moderate

Derivatives

Option Replication Using Put-Call Parity

An investor buys a European call and simultaneously sells a European put on the same non-dividend-paying stock, where both options have the same exercise price and the same expiration date. The combined position's payoff at expiration is most likely equivalent to that of:

Moderate

Derivatives

Option Replication Using Put-Call Parity

A non-dividend-paying stock trades at USD 48.00. A one-year European put option on the stock with an exercise price of USD 50.00 trades at USD 2.75, and the annual risk-free rate is 4.00%. Using put-call parity, the no-arbitrage price of the one-year European call option with the same exercise price is closest to:

Very Difficult

Derivatives

Option Replication Using Put-Call Parity

A non-dividend-paying stock trades at USD 60.00. One-year European options on the stock with an exercise price of USD 60.00 trade at USD 8.00 for the call and USD 4.50 for the put, and the annual risk-free rate is 5.00%. Based on put-call parity, the arbitrage strategy and the riskless profit captured today, per share, are best described as:

Difficult

Derivatives

Option Replication Using Put-Call Parity

One-year European options on a non-dividend-paying asset share an exercise price of USD 100.00. The call trades at USD 6.20, the put trades at USD 3.05, and the annual risk-free rate is 3.00%. Using put-call forward parity, the one-year forward price of the asset implied by these option prices is closest to: