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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 31
Calculation – Delta-hedging with stock A trader is short 500 call options on a stock. Each call has delta ( 0.6 ). To create a delta-neutral position using the stock, the trader should:
Select an option first.
Correct answer: B — Sell 300 shares.
Explanation: Short 500 calls → position delta: [ \Delta_{\text{portfolio}} = -500 \times 0.6 = -300 ] To offset −300, trader must buy +300 shares (delta +1 each). Wait—sign check: Short call has negative delta, so portfolio delta = −300. To make total delta zero, need +300 from stock → buy 300 shares. So correct answer is A. A. Correct: Buy 300 shares to offset −300 delta. B. Incorrect: Selling shares would make delta more negative. C, D. Wrong quantities. (Correct answer: A)
Question 32
Theta of a long option position is usually:
Select an option first.
Correct answer: B — Negative, because time passing reduces time value.
Explanation: B. Correct: For long options, time decay usually reduces value, so theta is negative. A. Incorrect: Time passing rarely increases value for long options. C. Incorrect: Time is a key input. D. Incorrect: Both calls and puts typically have negative theta when long.
Question 33
For a call and a put on the same underlying with same strike and maturity, which statement about vega is correct?
Select an option first.
Correct answer: C — Call and put vegas are equal.
Explanation: C. Correct: For same underlying, strike, and maturity, call and put have the same vega. A, B. Incorrect: No systematic dominance. D. Incorrect: Vega is highest near at-the-money, not zero.
Question 34
Which combination of signs for rho is correct for standard European options?
Select an option first.
Correct answer: A — Call rho positive, put rho negative.
Explanation: A. Correct: Higher rates increase call value (positive rho) and decrease put value (negative rho). B–D. Opposite or incorrect sign patterns.
Question 35
Implied volatility is best described as:
Select an option first.
Correct answer: B — The volatility that makes the model option price equal to the market price.
Explanation: B. Correct: Implied volatility is the volatility input that reconciles a pricing model with the observed option price. A. Incorrect: That’s historical volatility. C, D. Not standard definitions of implied volatility.
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Question 36
A trader compares implied volatilities across strikes and maturities mainly to:
Select an option first.
Correct answer: B — Identify relative mispricing of options.
Explanation: B. Correct: Comparing implied vols across strikes/maturities helps spot rich/cheap options and structure trades. A. Risk-free rate is usually known from bond markets. C. Dividends are not inferred primarily from vol surfaces. D. Intrinsic value depends on spot vs strike, not volatility.
Question 37
Calculation – Black model for futures call (conceptual) In the Black model for pricing a European call on a futures contract, the underlying in the formula is:
Select an option first.
Correct answer: C — The current futures price.
Explanation: C. Correct: Black’s model uses the current futures price as the underlying input. A. Spot is not used directly in the standard futures option formula. B. Forward at maturity is not the input; we use today’s futures price. D. Strike is a separate parameter, not the underlying.
Question 38
In a two-period binomial model for a European call, the option value at time 0 can be expressed as:
Select an option first.
Correct answer: B — The discounted expected payoff using risk-neutral probabilities.
Explanation: Binomial pricing uses risk-neutral probabilities and discounts expected payoff at the risk-free rate. B is correct: Core idea of risk-neutral valuation. A: Ignores discounting and probabilities. C: Real-world probabilities are not needed for pricing under no-arbitrage. D: Ignores time value and optionality.
Question 39
In a binomial tree, early exercise of an American put may be optimal when:
Select an option first.
Correct answer: B — The put is deep in-the-money and interest rates are positive.
Explanation: For American puts, early exercise can be optimal when the put is deep in-the-money and interest rates are positive, because exercising early allows you to receive cash sooner and invest it. B is correct: Captures the main condition. A: Out-of-the-money options are not exercised. C: Dividend relevance is more critical for calls. D: American calls on non-dividend-paying stocks are generally not exercised early.
Question 40
Which assumption is part of the classic Black–Scholes–Merton option pricing framework?
Select an option first.
Correct answer: B — The underlying price follows a continuous lognormal process.
Explanation: BSM assumes the underlying follows a geometric Brownian motion, implying lognormal prices and continuous trading. B is correct: Core BSM assumption. A: Volatility is assumed constant. C: Trading is assumed continuous. D: Risk-free rate is assumed constant.
Question 41
In the Black–Scholes–Merton model for a non-dividend-paying stock, the delta of a European call option is:
Select an option first.
Correct answer: B — Between 0 and 1.
Explanation: Call delta on a non-dividend-paying stock lies between 0 and 1: it increases as the option moves deeper in-the-money. B is correct: Correct range. A, D: Negative deltas are for puts. C: Delta approaches 1 only for deep in-the-money calls.
Question 42
Gamma for an option position measures:
Select an option first.
Correct answer: C — The sensitivity of delta to changes in the underlying price.
Explanation: Gamma is the rate of change of delta with respect to the underlying price. C is correct: Standard definition. A: Describes vega. B: Describes theta. D: Describes rho.
Question 43
A trader is short a call option and delta-hedges using the underlying stock. The main residual risk after delta-hedging is:
Select an option first.
Correct answer: C — Gamma and vega risk.
Explanation: Delta-hedging neutralizes first-order price sensitivity, but curvature (gamma) and volatility sensitivity (vega) remain. C is correct: Both gamma and vega are important residual risks. A: Ignores gamma. B: Ignores vega. D: Rho is usually less significant for equity options.
Question 44
Theta for a long option position is typically:
Select an option first.
Correct answer: B — Negative, because time passing erodes time value.
Explanation: For long options, time decay usually reduces option value as expiration approaches, so theta is typically negative. B is correct: Time decay hurts long option holders. A: Opposite of reality. C: Time is a key factor. D: Both calls and puts usually have negative theta when long.
Question 45
Vega of an option is usually highest when:
Select an option first.
Correct answer: C — The option is at-the-money.
Explanation: At-the-money options are most sensitive to volatility changes, so they have the highest vega. C is correct: Standard property of vega. A, B: Deep ITM/OTM options have low vega. D: Very short-dated OTM options have little value and low vega.
Question 46
Rho for a European call option on a non-dividend-paying stock is generally:
Select an option first.
Correct answer: A — Positive, because higher rates increase call value.
Explanation: Higher interest rates make it more attractive to defer payment for the stock (via the call), increasing call value. A is correct: Correct sign. B: Applies to puts. C: Incorrect; rates do matter. D: Vega is usually more important than rho for equity options.
Question 47
A trader believes the market is overestimating future volatility of a stock. Which strategy is most consistent with this view?
Select an option first.
Correct answer: B — Sell options with high implied volatility.
Explanation: If implied volatility is too high relative to your view, options are overpriced; selling options aims to profit when implied volatility falls or realized volatility is lower. B is correct: Short volatility view. A: Would be appropriate if volatility is underestimated. C: Neutral, not exploiting the view. D: Long straddle is long volatility.
Question 48
A volatility index (like a broad equity volatility index) is typically interpreted as:
Select an option first.
Correct answer: B — A measure of implied volatility over a future horizon.
Explanation: Volatility indices are constructed from option prices and represent the market’s implied volatility over a specified future period. B is correct: Forward-looking implied volatility. A: Backward-looking. C, D: Different risk dimensions.
Question 49
FRAs settle:
Select an option first.
Correct answer: B — At the start of the underlying loan period
Explanation: FRAs settle upfront, discounted, at the start of the loan period. A: Incorrect timing. C: No such convention. D: Settlement always occurs, even if payoff is zero. Swaps (Interest Rate, Currency, Equity)
Question 50
Receiving index return and paying floating in an equity swap is equivalent to:
Select an option first.
Correct answer: A — Borrowing cash to buy the index
Explanation: Receive index return = long index. Pay floating = financing cost. → Synthetic leveraged equity position. Binomial Option Valuation
Question 51
American calls on non‑dividend stocks:
Select an option first.
Correct answer: B — Are never exercised early
Explanation: Why: Early exercise sacrifices time value and provides no dividend benefit.
Question 52
Two‑period binomial: S0 = 50, up = 1.2, down = 0.8. Middle node price?
Select an option first.
Correct answer: A — 48
Explanation: [ 50 \times 1.2 \times 0.8 = 48 ] Black–Scholes–Merton
Question 53
BSM assumes:
Select an option first.
Correct answer: B — Constant volatility
Explanation: Key BSM assumptions include: Lognormal stock prices Constant volatility Continuous trading Constant risk‑free rate No jumps Thus B is correct.
Question 54
A European put’s delta is:
Select an option first.
Correct answer: B — Negative
Explanation: Put delta is always negative because put value decreases when stock price rises.
Question 55
If volatility increases, the value of a European call:
Select an option first.
Correct answer: B — Increases
Explanation: Higher volatility increases the chance of finishing in‑the‑money → call value rises.
Question 56
Gamma is highest for:
Select an option first.
Correct answer: C — ATM options
Explanation: Gamma peaks when the option is at‑the‑money, because small price changes most affect probability of finishing ITM.
Question 57
A delta‑neutral portfolio still has risk due to:
Select an option first.
Correct answer: C — Gamma and vega
Explanation: Delta‑neutral hedges only first‑order price risk. Remaining risks: Gamma (curvature) Vega (volatility sensitivity)
Question 58
Short 1,000 calls, delta = 0.4. Shares needed to delta‑hedge?
Select an option first.
Correct answer: A — Buy 400
Explanation: Short calls → delta = −400 → buy 400 shares.
Question 59
Theta for long options is usually:
Select an option first.
Correct answer: B — Negative
Explanation: Long options lose time value as expiration approaches → theta is negative.
Question 60
Vega measures sensitivity to:
Select an option first.
Correct answer: B — Volatility
Explanation: Vega = ∂OptionValue / ∂Volatility.
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