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CFA Level II Derivatives Practice Questions

Official outline
CFA Institute 2026 Level II Topic Outlines (learning outcomes)
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8
Updated
Nov 3, 2026

  1. Question 1, medium

    An analyst explains why an American put on a non-dividend-paying stock can be rationally exercised early even though an American call on the same stock should not be. Which reason is most accurate?

    • A.A put holder receives the stock's dividends, which exceed the option's time value
    • B.A put's time value rises as it moves deeper into the money, making early exercise a way to realize that gain
    • C.Put payoffs are unbounded as the stock falls, so exercising early locks in a larger payoff
    • D.Maximum put payoff is capped at the strike, so receiving it early and earning interest can outweigh remaining time value when deep in the money
    Show answer and explanationHide answer

    Correct answer: D. Maximum put payoff is capped at the strike, so receiving it early and earning interest can outweigh remaining time value when deep in the money

    A put's value cannot exceed X, and when the stock is near zero the put is worth almost its payoff. Exercising early lets the holder invest the strike proceeds at the risk-free rate, which can exceed the small remaining time value.

    • A. The stock in this example pays no dividends, and put holders do not receive them in any case.
    • B. Time value of a put shrinks as it goes deep in the money, which is why early exercise can be optimal.
    • C. A put's payoff is bounded by the strike because the stock price cannot fall below zero.
    • D. Correct: capped payoff plus interest on the strike can make early exercise optimal.

  2. Question 2, hard

    Analyst Dana observes add-on reference rates on a 360-day basis: 3.00% for 180 days and 3.40% for 270 days. She wants the rate implied for a 90-day loan that begins in 180 days, which is the fair rate on a 6x9 forward rate agreement. What is it?

    • A.4.20%
    • B.3.80%
    • C.4.14%
    • D.3.40%
    Show answer and explanationHide answer

    Correct answer: C. 4.14%

    Forward rate = [(1 + 0.034 x 270/360)/(1 + 0.03 x 180/360) - 1] x 360/90 = (1.0255/1.015 - 1) x 4 = 0.010345 x 4 = 4.14%. The longer deposit equals the shorter deposit rolled into the forward.

    • A. Takes the difference in interest amounts (2.55% - 1.50%) without dividing by the growth factor of the shorter period.
    • B. Extrapolates linearly (2 x 3.40% - 3.00%), which is not a no-arbitrage forward rate.
    • C. Correct: (1.0255/1.015 - 1) x 4 = 4.14%.
    • D. Reports the 270-day rate itself, ignoring the 180 days already covered.

  3. Question 3, medium

    Investor Sam holds an American call with three months to expiration on a stock that pays no dividends. The stock has risen sharply and the call is deep in the money. Sam is tempted to exercise now to lock in the intrinsic value. What is the best assessment?

    • A.Early exercise is preferred, since deep in-the-money options lose their time value to exercise
    • B.Early exercise is preferred, because the stock could fall before expiry and erase the intrinsic value
    • C.Early exercise is neutral, because the American call is worth the same as a European call after exercise
    • D.Early exercise gives up time value and interest on the strike, so sell the call or hold it
    Show answer and explanationHide answer

    Correct answer: D. Early exercise gives up time value and interest on the strike, so sell the call or hold it

    With no dividends, an American call is worth more unexercised than exercised: the call's price exceeds S - X, which includes the interest earned on the exercise price. Selling or holding captures that value; the American call equals its European value.

    • A. Time value does not vanish through holding; exercise is what discards it.
    • B. Selling the call also protects against a decline, and retains the time value.
    • C. The values are equal before exercise, but exercise converts the option to intrinsic value only, which is less.
    • D. Correct: exercising throws away time value and interest on the strike.

  4. Question 4, hard

    A firm entered a swap two years ago as the fixed-rate receiver at 4.5% on a notional of USD 10 million, with annual payments and two years remaining. The current par swap rate for two years is 4.0%, and the discount factors are 0.9615 for one year and 0.9246 for two years. What is the swap's value to the firm?

    • A.USD 100,000
    • B.USD 94,305
    • C.-USD 94,305
    • D.USD 50,000
    Show answer and explanationHide answer

    Correct answer: B. USD 94,305

    The firm receives 4.5% instead of the market 4.0%: value = (0.045 - 0.040) x 10,000,000 x (0.9615 + 0.9246) = 50,000 x 1.8861 = USD 94,305. Fixed receivers gain when swap rates fall.

    • A. Sums the two annual 50,000 differences without discounting them.
    • B. Correct: 50,000 x 1.8861 = 94,305.
    • C. Has the sign wrong; the fixed receiver at an above-market rate holds an asset.
    • D. Counts a single year of the rate difference.

  5. Question 5, medium

    An analyst uses put-call parity to build synthetic positions from European options on a non-dividend stock, with the same strike and expiration. Which combination replicates a long position in a zero-coupon bond whose face value equals the exercise price?

    • A.Long the stock, long a put, and short a call
    • B.Long the stock, short a put, and long a call
    • C.Short the stock, long a put, and long a call
    • D.Short the stock, long a call, and short a put
    Show answer and explanationHide answer

    Correct answer: A. Long the stock, long a put, and short a call

    Parity: c + X/(1+r)^T = p + S, so X/(1+r)^T = S + p - c. Holding the stock, buying a put and writing a call locks in the strike at expiration: a riskless bond payoff.

    • A. Correct: stock + put - call equals a risk-free bond.
    • B. Stock plus call minus put is c - p + S, which is twice the stock exposure less the bond.
    • C. Short stock plus call plus put does not eliminate price risk; it is a short position in the stock with a straddle.
    • D. Short stock plus call minus put equals borrowing at the risk-free rate, a short bond position.

  6. Question 6, hard

    A dealer is short 10,000 call options on a stock, each covering one share, and is delta hedged using the stock. The initial option delta is 0.55. After the stock rises, the delta increases to 0.65. What trade restores the delta hedge?

    • A.Sell 1,000 shares of the stock
    • B.Buy 6,500 more shares of the stock
    • C.Buy 1,000 more shares of the stock
    • D.Sell 5,500 shares of the stock
    Show answer and explanationHide answer

    Correct answer: C. Buy 1,000 more shares of the stock

    A short call position has delta of -0.55 x 10,000 = -5,500 shares, hedged with 5,500 shares long. At delta 0.65 the hedge needs 6,500 shares, so buy 1,000 more. Rising gamma means the hedge must be adjusted after price moves.

    • A. Selling reduces the hedge when the exposure has increased.
    • B. Buys the entire new hedge on top of the existing 5,500 shares, over-hedging.
    • C. Correct: 6,500 required less 5,500 held equals 1,000 more shares.
    • D. Unwinding most of the hedge would leave the short call exposure unprotected.

  7. Question 7, easy

    A European call on a non-dividend-paying stock sells for 6.20. The stock trades at 50.00, the exercise price is 50.00, and the option expires in one year. The annual risk-free rate is 4% with annual compounding. According to put-call parity, what is the value of the European put with the same terms?

    • A.6.20
    • B.8.12
    • C.8.20
    • D.4.28
    Show answer and explanationHide answer

    Correct answer: D. 4.28

    Put-call parity: p = c - S + X/(1+r)^T = 6.20 - 50.00 + 50.00/1.04 = 6.20 - 50.00 + 48.08 = 4.28. The exercise price must be discounted at the risk-free rate because a long call plus a bond must equal a long put plus the stock.

    • A. Uses the undiscounted exercise price: 6.20 - 50.00 + 50.00.
    • B. Adds the stock and subtracts the present value of the exercise price: 6.20 + 50.00 - 48.08.
    • C. Compounds the exercise price forward instead of discounting it (50 x 1.04 = 52).
    • D. Correct: 6.20 - 50.00 + 48.08 = 4.28.

  8. Question 8, easy

    A stock trades at 100.00. An analyst prices a one-year forward contract on it. The annual risk-free rate is 5%, and the stock is expected to pay a single dividend of 3.00 in six months. Using annual compounding, what is the no-arbitrage forward price?

    • A.102.00
    • B.105.00
    • C.101.93
    • D.108.07
    Show answer and explanationHide answer

    Correct answer: C. 101.93

    F = S(1+r)^T - FV(dividend) = 100(1.05) - 3.00(1.05)^0.5 = 105.00 - 3.0741 = 101.93. Dividends received by the stock holder, but not by the forward holder, reduce the forward price.

    • A. Subtracts the dividend without compounding it forward to the contract's expiration.
    • B. Ignores the dividend and prices the forward as spot compounded for one year.
    • C. Correct: 105.00 - 3.07 = 101.93.
    • D. Adds the compounded dividend instead of subtracting it.

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