You’re on a roll
Create a free account to save your CFA progress, track your accuracy by topic, and pick up right where you left off.
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 421
The breakeven price for a call option buyer is:
Select an option first.
Correct answer: B — Strike price plus premium paid
Explanation: ✔ Why correct: A call buyer breaks even when the underlying price at expiration equals strike + premium. Only above this level does the buyer profit. ✘ Why others are wrong: A is the breakeven for a put buyer. C mixes concepts. D ignores the cost of the premium.
Question 422
Theta in options refers to:
Select an option first.
Correct answer: B — The rate at which an option loses time value as expiration approaches
Explanation: ✔ Why correct: Theta measures time decay — the erosion of time value each day. Options with high theta lose value quickly as expiration approaches. ✘ Why others are wrong: A is rho. C is vega. D is the risk-neutral probability (N(d2) for calls).
Question 423
Implied volatility is:
Select an option first.
Correct answer: B — The volatility implied by the current market price of an option, given all other inputs
Explanation: ✔ Why correct: Implied volatility is backed out of the option pricing model using the observed market price. It represents the market's consensus forecast of future volatility. ✘ Why others are wrong: A is historical/realized volatility. C is not a standard term. D is not implied volatility.
Question 424
A higher underlying asset volatility increases the value of:
Select an option first.
Correct answer: C — Both call and put options
Explanation: ✔ Why correct: Volatility increases the probability of large moves in either direction. Since options have asymmetric payoffs (limited downside, unlimited upside for the buyer), higher volatility benefits both calls and puts. ✘ Why others are wrong: A and B are partial. D is incorrect; volatility is one of the key inputs to option pricing.
Question 425
An increase in the risk-free interest rate will generally:
Select an option first.
Correct answer: B — Increase call option prices and decrease put option prices
Explanation: ✔ Why correct: Higher risk-free rates increase the forward price of the underlying, benefiting calls. They also reduce the present value of the strike price, further helping calls and hurting puts (rho effect). ✘ Why others are wrong: A is backwards. C is wrong. D is incorrect since calls and puts react differently.
Get the full CFA question bank — free
Drop your email and we'll send you fresh CFA practice questions, fully worked solutions and exam-deadline reminders. No spam — unsubscribe in one click.
Want to save your score and take a full mock exam? Create a free account →
Question 426
For a deep in-the-money call option, the delta approaches:
Select an option first.
Correct answer: C — Positive one
Explanation: ✔ Why correct: A deep ITM call behaves almost like the stock — it moves dollar-for-dollar with the underlying. Delta approaches 1. ✘ Why others are wrong: A is a deep OTM call. B is a deep ITM put. D is the ATM approximation.
Question 427
Which of the following factors increases the value of a put option?
Select an option first.
Correct answer: B — Decrease in the underlying asset price
Explanation: ✔ Why correct: A put gains value when the underlying falls (moves below the strike). Lower underlying price increases intrinsic value for ITM puts. ✘ Why others are wrong: A hurts put value. C reduces time value. D reduces the probability of a large move.
Question 428
The breakeven for a put option buyer is:
Select an option first.
Correct answer: B — Strike price − premium paid
Explanation: ✔ Why correct: Put buyer breaks even when S_T = K − premium. If the price falls to this level, the put's payoff exactly covers the premium paid. ✘ Why others are wrong: A is the call breakeven. C includes spot incorrectly. D ignores premium cost.
Question 429
What is the maximum profit for a naked (uncovered) put writer?
Select an option first.
Correct answer: C — The premium received
Explanation: ✔ Why correct: The put writer receives the premium upfront. If the option expires worthless (S_T ≥ K), the full premium is the profit. That is the maximum gain. ✘ Why others are wrong: A applies to call buyers. B overstates. D is the put buyer's max gain, not the writer's.
Question 430
A long straddle involves:
Select an option first.
Correct answer: B — Buying both a call and a put at the same strike and expiration
Explanation: ✔ Why correct: A long straddle profits from large moves in either direction. The investor buys both a call and a put, often ATM, expecting a significant price swing. ✘ Why others are wrong: A creates a synthetic forward. C is a synthetic short. D is a call spread. Option Pricing
Question 431
According to the Black-Scholes-Merton model, the key inputs for pricing a European call option include all of the following EXCEPT:
Select an option first.
Correct answer: C — Expected return of the underlying
Explanation: ✔ Why correct: The BSM model is risk-neutral; it does not require the expected return of the underlying. The five BSM inputs are: S, K, T, r (risk-free rate), and σ (volatility). ✘ Why others are wrong: A, B, and D are all BSM inputs.
Question 432
In the binomial option pricing model, a one-period tree assumes the asset price can:
Select an option first.
Correct answer: B — Either go up by factor u or down by factor d
Explanation: ✔ Why correct: The binomial model simplifies the price process to two outcomes each period: an up move (×u) or a down move (×d). This allows backward induction to price the option. ✘ Why others are wrong: A is the continuous BSM assumption. C allows only one direction. D is a trinomial model.
Question 433
If implied volatility increases while all other factors remain constant, call option prices will:
Select an option first.
Correct answer: C — Increase
Explanation: ✔ Why correct: Vega is positive for both calls and puts. Higher volatility increases the probability of a favorable large move, raising the option premium. ✘ Why others are wrong: A is wrong. B ignores vega. D is wrong; the relationship is predictable and positive.
Question 434
The lower bound for a European call option on a non-dividend-paying stock is:
Select an option first.
Correct answer: C — Max(S − PV(K), 0)
Explanation: ✔ Why correct: The lower bound = max(S − PV(K), 0). If C < S − PV(K), an arbitrage exists: buy the call, short the stock, and invest PV(K) at the risk-free rate. ✘ Why others are wrong: A is too low. B doesn't discount the strike. D is the put lower bound.
Question 435
A call option's value is always at least equal to its intrinsic value because:
Select an option first.
Correct answer: C — A rational investor will not sell an option below intrinsic value since it could be immediately exercised for a profit
Explanation: ✔ Why correct: If a call were priced below its intrinsic value (S − K), an arbitrageur would buy the call, immediately exercise it, and lock in a riskless profit. Market forces prevent this. ✘ Why others are wrong: A applies to American options specifically. B is correct conceptually but C is the precise arbitrage argument. D is not a pricing determinant.
Question 436
Early exercise of an American call on a non-dividend-paying stock is:
Select an option first.
Correct answer: B — Never optimal because the option can always be sold for at least its intrinsic value
Explanation: ✔ Why correct: An American call on a non-dividend-paying stock should never be exercised early. The time value is always non-negative, so selling the option is always at least as good as exercising. ✘ Why others are wrong: A ignores the lost time value. C understates the always-positive time value. D is wrong; exercise is the holder's choice.
Question 437
Early exercise of an American put can be rational when:
Select an option first.
Correct answer: B — The put is deep in the money and the time value of waiting is less than the interest earned on the exercise proceeds
Explanation: ✔ Why correct: A deep ITM put may be worth exercising if the gain from receiving K early (and investing it) exceeds the remaining time value of the option. ✘ Why others are wrong: A is an OTM put. C and D do not specifically trigger early exercise.
Question 438
The volatility smile refers to:
Select an option first.
Correct answer: B — The pattern where implied volatility is higher for OTM options than for ATM options
Explanation: ✔ Why correct: Empirically, implied volatility is not constant across strikes. OTM puts and calls often have higher implied volatility than ATM options, creating a 'smile' shape in the IV curve. ✘ Why others are wrong: A is not the definition. C and D are market phenomena, not the volatility smile.
Question 439
The volatility skew (smirk) in equity options refers to:
Select an option first.
Correct answer: B — Higher implied volatility for lower-strike (OTM put) options than higher-strike options
Explanation: ✔ Why correct: In equity markets, OTM put options (left skew) typically have higher implied volatility than OTM calls. This reflects demand for downside protection and fear of crashes. ✘ Why others are wrong: A is the reverse. C is a term structure issue. D would be a flat smile.
Question 440
Under the BSM model, delta of a European call option equals:
Select an option first.
Correct answer: B — N(d1)
Explanation: ✔ Why correct: Delta_call = N(d1) in the BSM model. It represents the hedge ratio — the amount of stock needed to replicate the option. ✘ Why others are wrong: A is used in the call price formula for a different purpose. C is put delta. D involves present-value discounting.
Question 441
In the BSM model, N(d2) represents:
Select an option first.
Correct answer: B — The risk-neutral probability that the call option expires in the money
Explanation: ✔ Why correct: N(d2) is the risk-neutral probability that S_T > K at expiration — i.e., the call finishes in the money. N(d1) is the delta (hedge ratio). ✘ Why others are wrong: A is N(d1). C would be N(−d2). D is a monetary value, not a probability.
Question 442
The replicating portfolio approach to option pricing works because:
Select an option first.
Correct answer: B — A specific combination of the underlying and risk-free borrowing replicates the option payoff exactly
Explanation: ✔ Why correct: By constructing a portfolio of Δ shares and B in bonds that exactly matches the option payoffs in all scenarios, the option must be worth exactly the cost of this replicating portfolio (no arbitrage). ✘ Why others are wrong: A is not required. C is a special case. D is wrong.
Question 443
An option with positive vega will increase in value when:
Select an option first.
Correct answer: C — The implied volatility of the underlying increases
Explanation: ✔ Why correct: Vega is the sensitivity to volatility. All long option positions (calls and puts) have positive vega and gain value when volatility rises. ✘ Why others are wrong: A relates to delta. B relates to theta (indirectly). D relates to rho.
Question 444
A delta-neutral portfolio has been created. The portfolio will still lose value if:
Select an option first.
Correct answer: B — The underlying price makes a large move in either direction and gamma is negative
Explanation: ✔ Why correct: A short gamma position loses money when the underlying moves significantly in either direction, because delta hedging can't keep up with large moves. Theta offsets this to some degree. ✘ Why others are wrong: A benefits a short gamma/long theta portfolio. C hurts long vega, not just delta-neutral. D affects rho.
Question 445
The maximum profit on a bull call spread is:
Select an option first.
Correct answer: C — Difference between the two strikes minus the net premium paid
Explanation: ✔ Why correct: Max profit = (K_high − K_low) − net premium. It is capped because the short call offsets gains above K_high. ✘ Why others are wrong: A is uncapped for a simple long call. B is the maximum loss, not gain. D is not the profit formula.
Question 446
A short straddle profits most when:
Select an option first.
Correct answer: B — The underlying stays near the strike price through expiration
Explanation: ✔ Why correct: A short straddle (selling ATM call + put) collects maximum premium if the underlying stays near the strike and both options expire worthless. ✘ Why others are wrong: A is when a long straddle profits. C hurts the short straddle. D is a directional bet.
Question 447
The covered call strategy generates income but limits upside because:
Select an option first.
Correct answer: B — The short call obligates the investor to deliver shares at the strike if exercised
Explanation: ✔ Why correct: The short call becomes a liability if the stock rises above the strike, requiring the investor to sell at the strike (capping upside), but the premium offsets losses down to the stock's breakeven. ✘ Why others are wrong: A is backward; covered call generates income. C dividends belong to the stockholder. D describes a cash-secured put.
Question 448
A butterfly spread is designed to:
Select an option first.
Correct answer: B — Profit from low volatility with limited risk
Explanation: ✔ Why correct: A long butterfly (buy 1 low-strike call, sell 2 ATM calls, buy 1 high-strike call) profits most when the underlying is at the middle strike at expiration. It benefits from low volatility. ✘ Why others are wrong: A is a straddle/strangle strategy. C is impossible for a derivative strategy. D is achieved with puts or futures.
Question 449
Delta hedging means:
Select an option first.
Correct answer: B — Maintaining a portfolio that is insensitive to small changes in the underlying price
Explanation: ✔ Why correct: A delta-neutral position has Δ_portfolio ≈ 0. Small changes in the underlying price do not change the portfolio value. This requires dynamic rebalancing as delta changes. ✘ Why others are wrong: A is a different hedging concept. C is not the definition. D is duration matching for bonds.
Question 450
A long call condor profit is maximum when:
Select an option first.
Correct answer: B — The underlying stays within a middle range (between the two middle strikes) at expiration
Explanation: ✔ Why correct: A long condor (buy outer strikes, sell inner strikes) profits when the underlying stays within a moderate range. It is a low-volatility bet with limited risk and reward. ✘ Why others are wrong: A is a long straddle/strangle. C benefits long vega strategies. D is OTM for all components.
More free CFA topics
Economics2,066
Quantitative Methods1,213
Portfolio Management1,079
Fixed Income908
Financial Statement Analysis904
Corporate Issuers884
Portfolio Construction605
Alternative Investments540
Specialized Pathway - Private Markets500
Asset Allocation499
Equity390
Performance Measurement295
Specialized Pathway - Portfolio Management253
Derivatives and Risk Management131
Ten questions in
- The ones you miss are saved as a drill you can repeat
- Your place is kept, on this device and any other
- A streak, if that is the thing that gets you back tomorrow
Every question on this page stays free and open either way.