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Free Questions › CFA › Derivatives
Free CFA Derivatives Practice Questions & Answers
500 exam-style Derivatives questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 391
Derivatives market liquidity is typically highest for:
Select an option first.
Correct answer: B — Standardized, short-dated exchange-traded contracts in active markets
Explanation: ✔ Why correct: Standardization and short maturities create the most active trading — many participants want the same product at the same time, creating tight spreads and easy entry/exit. ✘ Why others are wrong: A, C, and D are niche, customized, or less actively traded instruments.
Question 392
Rehypothecation of collateral in derivatives means:
Select an option first.
Correct answer: A — The pledging of collateral that has already been pledged by another party, creating a chain of claims
Explanation: ✔ Why correct: Rehypothecation allows a party that receives collateral to reuse it as collateral for their own obligations. This creates interconnected chains of collateral claims that can amplify systemic risk. ✘ Why others are wrong: B is return of collateral. C is collateral transformation. D is haircut calculation. Advanced Topics
Question 393
A 'synthetic forward' using options is created by:
Select an option first.
Correct answer: A — Buying a call and selling a put at the same strike and expiration on the same underlying
Explanation: ✔ Why correct: Long call + short put at the same strike = synthetic long forward, by put-call parity. This replicates the payoff profile of a forward contract. ✘ Why others are wrong: B is a call spread (partially). C is a short straddle. D is a long straddle.
Question 394
The 'law of one price' in derivatives says:
Select an option first.
Correct answer: B — Two assets with identical future cash flows must have the same price today
Explanation: ✔ Why correct: The law of one price is the foundation of no-arbitrage pricing. If two assets produce identical cash flows in every state of the world, they must trade at the same price — otherwise riskless profit is available. ✘ Why others are wrong: A is too broad. C confuses convergence with continuous equality. D ignores time value differences.
Question 395
Forward volatility (vol) refers to:
Select an option first.
Correct answer: B — The implied volatility for a future time period, derived from the term structure of implied volatility
Explanation: ✔ Why correct: Forward vol is extracted from option prices at different maturities. It represents the market's expectation of volatility between two future dates, analogous to forward interest rates. ✘ Why others are wrong: A is historical vol. C is average vol across strikes. D is price vol of futures.
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Question 396
The risk-neutral measure (Q-measure) differs from the real-world measure (P-measure) in that:
Select an option first.
Correct answer: B — Under Q, all assets earn the risk-free rate in expectation, enabling discounting at r
Explanation: ✔ Why correct: Under the risk-neutral measure, expected returns of all assets equal the risk-free rate. This mathematical construction simplifies derivative pricing — no separate expected return estimate is needed. ✘ Why others are wrong: A is the opposite. C is nonsensical. D confuses P-measure attribution with Q-measure pricing.
Question 397
Convexity adjustment in interest rate derivatives is needed because:
Select an option first.
Correct answer: A — Bond prices have convex price-yield relationships that create systematic biases in futures pricing
Explanation: ✔ Why correct: Interest rate futures are affected by convexity: the correlation between futures mark-to-market and interest rate changes creates a systematic difference between futures and forward rates, requiring a convexity adjustment. ✘ Why others are wrong: B is a general option property, not rate futures. C is a cost adjustment. D is the tailing the hedge concept.
Question 398
Drift in the context of stochastic processes for derivative pricing refers to:
Select an option first.
Correct answer: B — The expected (average) rate of change of the asset price
Explanation: ✔ Why correct: In a stochastic differential equation (e.g., dS = μS dt + σS dZ), μ is the drift (expected return, deterministic component). In risk-neutral pricing, drift is replaced by r. ✘ Why others are wrong: A is the diffusion or random term. C is σ. D is correlation.
Question 399
The no-arbitrage condition in derivative pricing assumes:
Select an option first.
Correct answer: B — There are no riskless profit opportunities available
Explanation: ✔ Why correct: No-arbitrage does not require market efficiency broadly — it requires that riskless, costless profit opportunities do not persist. Any mispricing is instantly eliminated by arbitrageurs. ✘ Why others are wrong: A is market efficiency (broader). C is the risk-neutral measure assumption, not reality. D contradicts the stochastic nature of prices.
Question 400
In derivatives, the term 'theta-vega tradeoff' refers to:
Select an option first.
Correct answer: B — Long options positions having negative theta (time decay cost) and positive vega (volatility benefit)
Explanation: ✔ Why correct: Long options have positive vega (gain from higher volatility) but negative theta (lose from time decay). These two Greeks represent the classic cost-benefit of holding options. ✘ Why others are wrong: A is not a standard financial concept. C is a risk management action. D is wrong; they do not always offset.
Question 401
The Garman-Kohlhagen model is an extension of BSM used for pricing:
Select an option first.
Correct answer: C — European options on foreign currencies
Explanation: ✔ Why correct: Garman-Kohlhagen replaces the dividend yield in BSM with the foreign risk-free rate, treating the currency as a continuous dividend-paying asset. It prices European FX options. ✘ Why others are wrong: A uses BSM-based barrier pricing. B uses Black's model for futures options. D requires American option modifications.
Question 402
Black's model is commonly used for pricing:
Select an option first.
Correct answer: B — Options on futures and forward contracts
Explanation: ✔ Why correct: Black's model treats the futures/forward price as the underlying, applying a BSM-like formula. It is widely used for caps, floors, swaptions, and bond options. ✘ Why others are wrong: A uses standard BSM. C uses reduced-form or intensity models. D requires more complex path-dependent models.
Question 403
The Heston model improves on BSM by:
Select an option first.
Correct answer: B — Introducing stochastic volatility with mean reversion
Explanation: ✔ Why correct: The Heston model (1993) allows volatility to be stochastic, mean-reverting, and correlated with the price, capturing the volatility smile and skew that BSM cannot. ✘ Why others are wrong: A describes interest rate models. C describes jump-diffusion models (Merton 1976). D is not the Heston innovation.
Question 404
Which of the following best describes a 'volatility swap'?
Select an option first.
Correct answer: B — A contract where one party pays realized volatility and the other pays a fixed volatility (the strike)
Explanation: ✔ Why correct: A volatility swap has a payoff based on realized volatility vs. the fixed strike. It is a pure exposure to volatility (unlike variance swaps, which are proportional to variance = σ²). ✘ Why others are wrong: A is an interest rate swap. C is a VIX option. D is a VIX-linked note.
Question 405
The 'Greeks' of a portfolio of derivatives can be aggregated because:
Select an option first.
Correct answer: B — Greeks are partial derivatives and are additive across linear combinations of positions
Explanation: ✔ Why correct: Since Greeks are partial derivatives of value with respect to risk factors, and the value of a portfolio is the sum of position values, the Greeks of the portfolio are the sums of the individual Greeks (by linearity of differentiation). ✘ Why others are wrong: A is wrong. C is wrong; aggregation reveals risk but doesn't eliminate it. D is wrong.
Question 406
An importer will need to buy foreign currency in 6 months. To hedge this exposure using a forward, the importer should:
Select an option first.
Correct answer: B — Enter a long forward on the foreign currency
Explanation: ✔ Why correct: The importer has a future obligation to pay foreign currency (a short exposure). To hedge, they lock in the exchange rate by taking a long forward on the foreign currency. ✘ Why others are wrong: A would add to the risk. C and D do not directly offset the currency payable.
Question 407
A company that will need to borrow money in 3 months and fears interest rates will rise should:
Select an option first.
Correct answer: B — Buy an FRA (go long the FRA)
Explanation: ✔ Why correct: Buying an FRA locks in a borrowing rate. If rates rise, the FRA pays the difference, offsetting higher borrowing costs. ✘ Why others are wrong: A (selling the FRA) benefits if rates fall. C (receive-fixed swap) also pays if rates fall. D (put on bonds) profits when bond prices fall, i.e., rates rise, but is an option, not a direct hedge.
Question 408
A receiver swaption is analogous to a:
Select an option first.
Correct answer: A — Call option on a bond (gains value when rates fall / bond prices rise)
Explanation: ✔ Why correct: A receiver swaption (right to receive fixed) benefits when rates fall. Falling rates increase the present value of the fixed receipts, just like a call option on a bond gains value when the bond price rises. ✘ Why others are wrong: B is a payer swaption analogy. C and D are different instruments.
Question 409
A call option gives the buyer the right to:
Select an option first.
Correct answer: B — Buy the underlying asset at the strike price before or at expiration
Explanation: ✔ Why correct: A call is the right (not obligation) to purchase the underlying at the agreed strike price on or before expiration. ✘ Why others are wrong: A is a put option. C is a shareholder right. D describes a forward payoff.
Question 410
A put option gives the buyer the right to:
Select an option first.
Correct answer: B — Sell the underlying asset at the strike price before or at expiration
Explanation: ✔ Why correct: A put option grants the right to sell the underlying at the strike price. The put gains value when the underlying price falls below the strike. ✘ Why others are wrong: A is a call option. C and D are not option rights.
Question 411
An American option differs from a European option in that an American option:
Select an option first.
Correct answer: B — Can be exercised at any time up to and including expiration
Explanation: ✔ Why correct: American options allow early exercise. European options can only be exercised at the expiration date. Most exchange-traded equity options are American-style. ✘ Why others are wrong: A describes a European option. C is wrong; both styles trade worldwide. D is unrelated to exercise style.
Question 412
An option is said to be 'in the money' (ITM) when:
Select an option first.
Correct answer: B — The option has positive intrinsic value (exercising it immediately would produce a positive payoff)
Explanation: ✔ Why correct: A call is ITM when S > K. A put is ITM when S < K. The option has intrinsic value because immediate exercise produces a positive payoff. ✘ Why others are wrong: A confuses intrinsic value with time value. C is not the definition. D is unrelated.
Question 413
A call option with a strike price of $50 is at the money when the underlying asset price is:
Select an option first.
Correct answer: C — $50
Explanation: ✔ Why correct: At-the-money (ATM) means the underlying price equals the strike price. Neither exercise nor non-exercise produces a payoff. ✘ Why others are wrong: A is out of the money for a call (S < K). B is in the money (S > K). D is deep out of the money.
Question 414
Intrinsic value of a call option is calculated as:
Select an option first.
Correct answer: B — Max(S − K, 0)
Explanation: ✔ Why correct: Call intrinsic value = max(S − K, 0). It is the immediate exercise payoff, floored at zero because no rational holder would pay to exercise at a loss. ✘ Why others are wrong: A is put intrinsic value. C allows negative intrinsic value, which is wrong. D is circular (intrinsic + time value = premium, not this formula).
Question 415
Time value of an option is:
Select an option first.
Correct answer: B — The amount by which the option premium exceeds its intrinsic value
Explanation: ✔ Why correct: Time value = premium − intrinsic value. It reflects the probability that the option moves further in the money before expiration. It erodes as expiration approaches (theta decay). ✘ Why others are wrong: A is not the correct formula. C is part of option pricing models, not time value definition. D is wrong; ITM options can still have time value.
Question 416
The maximum loss for a call option buyer is:
Select an option first.
Correct answer: C — The premium paid
Explanation: ✔ Why correct: The most a call buyer can lose is the premium paid. If the option expires worthless, only the premium is lost. ✘ Why others are wrong: A is the risk for the naked call seller, not the buyer. B and D overstate the maximum loss.
Question 417
The maximum gain for a put option buyer is:
Select an option first.
Correct answer: B — The strike price minus the premium paid
Explanation: ✔ Why correct: The best outcome for a put buyer is the underlying falling to zero. Payoff = K − 0 = K; net of premium paid: K − premium. This is the maximum gain. ✘ Why others are wrong: A applies to call buyers. C is a description, not a calculation. D is what the seller receives.
Question 418
Writing (selling) a naked call option exposes the seller to:
Select an option first.
Correct answer: B — Unlimited losses if the underlying price rises sharply
Explanation: ✔ Why correct: A naked (uncovered) call seller must deliver the underlying if exercised. Since the underlying price can rise without limit, losses are theoretically unlimited. ✘ Why others are wrong: A is the maximum gain, not maximum loss. C understates the risk. D ignores the delivery obligation.
Question 419
A protective put strategy involves:
Select an option first.
Correct answer: A — Buying the underlying stock and buying a put option on it
Explanation: ✔ Why correct: A protective put is a long stock + long put combination. It provides downside protection (the put sets a floor) while maintaining upside participation. ✘ Why others are wrong: B is a different hedge. C is a collar setup. D is a short straddle.
Question 420
A covered call strategy consists of:
Select an option first.
Correct answer: B — Owning the underlying stock and selling (writing) a call option on it
Explanation: ✔ Why correct: A covered call is long stock + short call. The existing stock 'covers' the call obligation. The investor earns premium income but caps upside at the strike price. ✘ Why others are wrong: A is a short call with additional hedging. C is a long straddle. D is a naked put.
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