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 61
Rho for a European put is:
Select an option first.
Correct answer: B — Negative
Explanation: Implied Volatility & Vol Surfaces
Question 62
Implied volatility is:
Select an option first.
Correct answer: B — Forward‑looking
Explanation: IV reflects the market’s expectation of future volatility, not historical realized volatility.
Question 63
A volatility smile means:
Select an option first.
Correct answer: B — IV is highest at low and high strikes
Explanation: A smile shape means: High IV for deep ITM High IV for deep OTM Lower IV near ATM
Question 64
If implied volatility is “rich,” it means:
Select an option first.
Correct answer: B — Options are expensive
Explanation: “Rich” = overpriced relative to fair value.
Question 65
A trader comparing implied vol across markets is mainly looking for:
Select an option first.
Correct answer: B — Relative option mispricing
Explanation: Traders compare IVs to identify relative value arbitrage opportunities.
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 66
American put early exercise intuition Which situation most strongly supports early exercise of an American put on a non‑dividend‑paying stock?
Select an option first.
Correct answer: B — Deep in‑the‑money put, high interest rates, short time to maturity
Explanation: Early exercise of a put is attractive when: Put is deep in the money (intrinsic value high), Interest rates are high (you can invest proceeds), Little time value left (short time to maturity). A Long time to maturity means more time value to lose. C, D Not deep ITM, so early exercise less appealing.
Question 67
Discrete dividend in binomial tree A stock is expected to pay a known cash dividend during the life of a binomial tree. The standard way to incorporate this is to:
Select an option first.
Correct answer: B — Subtract the PV of the dividend from the stock price at the ex‑dividend node.
Explanation: For discrete known dividends, the stock price is reduced by the dividend amount at the ex‑dividend node (or you start with S₀ minus PV of dividends). A Ignoring is incorrect. C Strike is not adjusted. D That’s more for continuous yield modeling, not discrete cash dividends.
Question 68
Continuous dividend yield in binomial/BSM A stock pays a continuous dividend yield q. In a risk‑neutral framework, the expected growth rate of the stock price is:
Select an option first.
Correct answer: C — r − q
Explanation: Under risk‑neutral pricing with continuous dividend yield q, the stock’s expected growth rate is r − q. A Ignores dividends. B, D Wrong sign.
Question 69
BSM formula structure Which statement best describes the structure of the Black–Scholes–Merton formula for a European call on a non‑dividend‑paying stock?
Select an option first.
Correct answer: B — Stock price times a risk‑neutral probability minus discounted strike times another risk‑neutral probability.
Explanation: The BSM call price is: [ C = S_0 N(d_1) - K e^{-rT} N(d_2) ] Interpretation: stock price × risk‑neutral probability of exercise minus discounted strike × risk‑neutral probability of exercise. A Uses real‑world probabilities, not risk‑neutral. C, D Ignore the probability weighting.
Question 70
Interpretation of d1 In the BSM model, (d_1) is most commonly interpreted as:
Select an option first.
Correct answer: B — A standardized measure of how far the forward price is above the strike, adjusted for volatility and time.
Explanation: (d_1) is a standardized distance between the current forward price and the strike, scaled by volatility and time. A That’s closer to (N(d_2)) interpretation (under risk‑neutral). C Delta equals (N(d_1)) for a call, not (d_1) itself. D Gamma is a second derivative, unrelated to d1 directly.
Question 71
BSM with continuous dividends For a stock paying a continuous dividend yield q, the BSM formula for a European call is modified by:
Select an option first.
Correct answer: A — Replacing S₀ with (S_0 e^{-qT})
Explanation: With continuous dividend yield q, the call price becomes: [ C = S_0 e^{-qT} N(d_1) - K e^{-rT} N(d_2) ] So S₀ is replaced by (S_0 e^{-qT}). B Strike is not adjusted by q. C The adjustment is in the drift term and S₀ factor, not just discounting D Volatility is not directly adjusted by q.
Question 72
Black model for futures options In the Black model for a European call on a futures contract, the underlying input is:
Select an option first.
Correct answer: C — Futures price of the asset
Explanation: The Black model for options on futures uses the current futures price as the underlying. A, B Not the standard input for Black futures option model. D Discounting is applied to the payoff, not to the futures input.
Question 73
Caplet pricing intuition A caplet can be viewed as:
Select an option first.
Correct answer: C — A call option on an interest rate or reference rate.
Explanation: A caplet pays off when the reference rate exceeds a strike—economically a call on the interest rate. A, B Bond options are different instruments. D That describes a floorlet (put on rate).
Question 74
Floorlet pricing intuition A floorlet is best interpreted as:
Select an option first.
Correct answer: B — A put on an interest rate
Explanation: A floorlet pays when the reference rate falls below a strike—like a put on the interest rate. A That’s a caplet. C, D Bond options, not rate options.
Question 75
Futures option valuation intuition A call option on a futures contract is more sensitive to which of the following?
Select an option first.
Correct answer: B — Changes in the futures price
Explanation: The underlying of a futures option is the futures price, so the option’s value is primarily sensitive to changes in the futures price. A Spot affects futures, but the direct driver is futures. C, D Secondary effects.
Question 76
Swaption valuation intuition The value of a payer swaption increases when:
Select an option first.
Correct answer: C — Interest rates rise
Explanation: A payer swaption benefits from higher interest rates, because paying fixed becomes cheaper relative to receiving higher floating. A Lower rates favor receiver swaptions. B Lower volatility reduces option value. D Less time reduces optionality.
Question 77
Gamma‑neutral hedging A trader is long a large number of call options and wants to reduce gamma risk. Which action is most consistent with moving toward gamma neutrality?
Select an option first.
Correct answer: B — Sell calls or buy puts with similar maturities and strikes
Explanation: Gamma comes from options, not stock. To reduce net gamma, the trader can sell options (calls or puts) with offsetting gamma. A Increases gamma. C, D Stock has zero gamma; it changes delta but not gamma.
Question 78
Vega hedging A portfolio is long vega. To reduce sensitivity to volatility changes, the manager should:
Select an option first.
Correct answer: B — Sell options with positive vega
Explanation: Long vega means the portfolio benefits from higher volatility. To reduce vega, the manager should sell options (which have positive vega). A Increases vega. C, D Underlying has zero vega.
Question 79
Rho magnitude vs other Greeks For short‑dated equity options, rho is typically:
Select an option first.
Correct answer: B — Less important than delta and gamma
Explanation: For short‑dated equity options, sensitivity to interest rates (rho) is usually small compared with delta and gamma. A Overstates rho’s importance. C Obviously false. D Rho is not zero, just small.
Question 80
Theta behavior near expiration For an at‑the‑money option, as time to expiration approaches zero, theta tends to:
Select an option first.
Correct answer: A — Increase in magnitude (more negative for long options)
Explanation: Near expiration, time decay accelerates, especially for at‑the‑money options. Long options experience more negative theta as expiry approaches. B, D Opposite of reality. C Sign is not determined by call vs put; both typically have negative theta when long.
Question 81
Volatility skew Volatility skew in equity index options typically reflects:
Select an option first.
Correct answer: B — Higher implied volatility for out‑of‑the‑money puts than calls
Explanation: Equity index markets often show a “smirk” or skew where out‑of‑the‑money puts have higher implied volatility than calls—reflecting demand for downside protection. A Reversed. C, D Would be true under constant volatility assumptions, not in practice.
Question 82
Volatility surface interpretation A volatility surface plots implied volatility as a function of:
Select an option first.
Correct answer: C — Strike and maturity
Explanation: A volatility surface is a 3D representation: implied volatility vs strike and time to maturity. A, B Only one dimension. D Underlying price is implicit but not the axes of the surface.
Question 83
A receiver swaption is most valuable when:
Select an option first.
Correct answer: B — Market swap rates are much lower than the strike.
Explanation: Why B is right: Receiver swaption = right to receive fixed at strike (K). It is valuable when market fixed rates fall below K, so you receive above‑market fixed payments. Why others are wrong: A: That benefits payer swaptions. C: Curve shape alone doesn’t determine value. D: Deep out‑of‑the‑money options have low value.
Question 84
A floorlet is best described as:
Select an option first.
Correct answer: B — A put option on an interest rate.
Explanation: Why B is right: A floorlet pays when the reference rate falls below the strike, like a put on the rate. Why others are wrong: A: That describes a caplet. C, D: Those are options on bonds, not rates.
Question 85
The Black model is commonly used to value:
Select an option first.
Correct answer: B — Options on forwards and futures, including caps, floors, and swaptions.
Explanation: Why B is right: The Black model is widely used for options on forwards/futures, including interest rate caps, floors, and swaptions. Why others are wrong: A: Equity options are usually priced with BSM. C: Black model is for European‑style options. D: Not designed for exotic path‑dependent structures.
Question 86
The gamma of a European option under BSM (for both calls and puts) is:
Select an option first.
Correct answer: A — Always positive and equal for calls and puts.
Explanation: Why A is right: Gamma measures curvature of option value vs. stock price. Under BSM, gamma is positive and identical for calls and puts with same strike and maturity. Why others are wrong: B: Gamma is not negative. C: Sign does not differ by type. D: Gamma is small but not zero for deep ITM.
Question 87
The rho of a European call option is:
Select an option first.
Correct answer: A — Typically positive, measuring sensitivity to interest rates.
Explanation: Why A is right: Higher interest rates increase call values (you defer paying the strike), so rho for calls is positive. Why others are wrong: B: That describes puts. C: Interest rates do matter. D: Vega is usually larger in magnitude than rho.
Question 88
In a two‑period binomial model with dividends, the usual approach is to:
Select an option first.
Correct answer: B — Subtract the present value of dividends from the stock price before building the tree.
Explanation: Why B is right: Known dividends are treated as separate cash flows; we often work with the stock price net of PV of dividends when building the binomial tree. Why others are wrong: A: Dividends can materially affect value. C: Strike is not adjusted this way. D: Stock must be in the tree.
Question 89
The early exercise premium of an American put is:
Select an option first.
Correct answer: A — The difference between the American and European put prices.
Explanation: Why A is right: Early exercise premium = American put value – European put value. It reflects the value of the right to exercise early. Why others are wrong: B: That’s not the standard definition. C: Unrelated. D: It is often positive for puts.
Question 90
A volatility term structure refers to:
Select an option first.
Correct answer: B — Volatility as a function of time to expiration.
Explanation: Why B is right: Term structure of volatility = how implied volatility varies with maturity. Why others are wrong: A: That’s a volatility smile/skew. C, D: Not standard terminology.
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.