Derivatives. 14 question(s) in this unit's pool
(2 above the exam). Free up to ten a day; the coach picks which ones based on what you have
already answered and when each is next due.
Pick an answer, say how sure you are, then reveal. Every wrong choice gets its own
explanation. Questions you have already answered correctly and confidently stay out of the way until they
are due for review again.
Question 1Exam level
An investor buys a call option on a stock with a strike price of $50 and pays a premium of $4. At expiration, the stock price is $58. The profit per share to the call buyer is closest to:
How sure are you?
Correct: A. The correct answer is $4. Profit = max(S - X, 0) - premium = max(58 - 50, 0) - 4 = 8 - 4 = $4. The payoff is $8 but the profit nets out the $4 premium paid..
B. This is the gross payoff. Max(58-50, 0) = $8. You might stop here and forget to subtract the premium. Payoff is gross. Profit requires subtracting the premium cost of acquiring the option.
C. A candidate might think the premium makes the position a net loss without computing the payoff first. The call is exercised for a positive payoff of $8, which more than offsets the $4 premium.
Unit: pricing-and-valuation-of-options
Question 2Exam level
A put option has a strike price of $60. The stock is currently trading at $55. The intrinsic value of the put is closest to:
How sure are you?
Correct: A. The correct answer is $5. Intrinsic value of a put = max(X - S, 0) = max(60 - 55, 0) = $5. The put is in-the-money by $5..
B. A candidate applying call-option logic would write max(S - X, 0) = max(55 - 60, 0) = 0. For puts, intrinsic value = max(X - S, 0). The formula runs in the opposite direction from calls.
C. A candidate might compute 55 - 60 = -5 without applying the max(.,0) floor. Intrinsic value is floored at zero. Options never have negative intrinsic value. They simply expire worthless.
Unit: pricing-and-valuation-of-options
Question 3Exam level
A stock currently trades at $45. An investor writes (sells) a put option with a strike price of $50 and receives a premium of $6. If the stock price falls to $38 at expiration, the profit to the put writer is closest to:
How sure are you?
Correct: A. The correct answer is -$6. Put writer profit = premium received - max(X - S, 0) = 6 - max(50 - 38, 0) = 6 - 12 = -$6. The buyer exercises, forcing the writer to buy at $50 when the stock is worth $38..
B. A candidate focused only on the premium received, forgetting the put was exercised against the writer. The put is deep in-the-money at $38 vs $50 strike. The writer is obligated to buy at $50, losing $12 before netting the premium.
C. Arithmetic error: computing 45 - 38 = 7 and using the original stock price instead of the strike. The relevant comparison is strike ($50) vs expiration price ($38), not current price vs expiration price.
Unit: pricing-and-valuation-of-options
Question 4Exam level
Which of the following statements best describes a long call position?
How sure are you?
Correct: A. The correct answer is The right to buy a specified quantity at the exercise price before or at expiration. A call option gives the buyer (long) the right. Not the obligation. To BUY the underlying at the strike price..
B. This describes the short put writer's obligation. 'obligation' sounds right because options involve obligations somewhere. The BUYER of a call has a right, not an obligation. The writer of a put has the obligation to buy if exercised.
C. This describes the short call writer's obligation, which is the counterparty to the long call. Long = buyer = right holder. Short = writer = obligation bearer. The question asks about long (buyer) position.
Unit: pricing-and-valuation-of-options
Question 5Exam level
A call option with a strike price of $75 is trading at $9. The underlying stock is at $80. The time value of the option is closest to:
How sure are you?
Correct: A. The correct answer is $4. Intrinsic value = max(S - X, 0) = max(80 - 75, 0) = $5. Time value = option price - intrinsic value = 9 - 5 = $4..
B. This is the intrinsic value. Candidates who correctly compute max(80-75,0) confuse intrinsic for time value. Intrinsic value = $5. Time value = $9 - $5 = $4. These are different components.
C. Adding the stock-strike gap ($5) to the option price ($9). Nonsensical but arithmetically close. Time value is never larger than the option price. Adding intrinsic to the total price is a double-count error.
Unit: pricing-and-valuation-of-options
Question 6Exam level
At expiration, the payoff to the writer of a call option with a strike price of $40 when the stock price is $47 is closest to:
How sure are you?
Correct: A. The correct answer is -$7. Short call payoff at expiration = -max(S - X, 0) = -max(47 - 40, 0) = -$7. The writer must deliver shares at $40 when they are worth $47..
B. This is the BUYER's payoff, not the writer's. Candidates who compute long call payoff and forget to flip the sign. Short positions have mirror-image payoffs. Writer's payoff = negative of buyer's payoff.
C. The strike price itself is a plausible-looking distractor. The payoff is not the strike price. It is the loss from being forced to sell at $40 when shares are worth $47.
Unit: pricing-and-valuation-of-options
Question 7Harder
All else equal, which of the following changes would most likely increase the value of a put option?
How sure are you?
Correct: A. The correct answer is An increase in volatility of the underlying. Increased volatility increases the value of BOTH calls and puts because it raises the probability of the option expiring deeply in-the-money..
B. You might sometimes confuse time decay direction, or think 'closer to expiry = closer to payout.'. Less time means less opportunity for favorable moves. Time value erodes as expiration approaches.
C. Higher rates are often associated with higher returns on financial instruments generally. Higher risk-free rates REDUCE put value because the present value of the exercise price (what the put delivers) falls. This is the #1 tested counterintuitive factor direction.
Unit: pricing-and-valuation-of-options
Question 8Exam level
A stock is trading at $100. An investor holds 100 shares and buys 1 put contract (100 shares) with strike price $95 for a premium of $3 per share. The maximum loss on the combined stock-plus-put position is most likely:
How sure are you?
Correct: A. The correct answer is $800. Maximum loss = (current price - strike price + premium) x shares = (100 - 95 + 3) x 100 = $800. The put floors the sale price at $95, so the maximum loss is the $5 decline allowed plus the $3 premium cost..
B. Only counting the premium cost ($3 x 100 shares), forgetting the $5 gap between current price and strike. The put does not protect at exactly the current price. It protects at the strike. The $5 unprotected gap is a deductible.
C. Confusing unhedged stock exposure (which is indeed large) with the hedged position. The whole point of the protective put is to cap the downside. The put converts unlimited stock downside into a bounded loss.
Unit: pricing-and-valuation-of-options
Question 9Exam level
An investor writes a put option on a stock with a strike price of $30 and receives a premium of $4. The maximum profit to the put writer is closest to:
How sure are you?
Correct: A. The correct answer is $4. The maximum profit to a put writer occurs when the put expires worthless (stock price at or above the strike at expiration). In that case, the writer keeps the entire $4 premium and has no obligation..
B. The strike price itself. You might confuse the maximum exercise payout with the writer's maximum gain. The $30 strike is the maximum obligation for the writer, not the maximum gain. Maximum profit is always capped at premium received for any option seller.
C. Strike minus premium (30 - 4 = 26). This is actually the break-even price, not the maximum profit. $26 is the break-even stock price for the put writer. Maximum profit is the premium received when the put expires worthless.
Unit: pricing-and-valuation-of-options
Question 10Exam level
Which of the following positions most likely has theoretically unlimited maximum loss?
How sure are you?
Correct: A. The correct answer is Short call. A short call writer has unlimited loss potential because the underlying stock price has no theoretical upper limit. If the stock rises to $200 with a $50 strike, the writer loses $150 per share minus the premium received..
B. Buying a put also has loss potential. But again it is limited to the premium paid. Long put maximum loss = premium paid. Even if the put expires worthless, you lose only what you paid.
C. Selling options is risky, and candidates lump all short positions as equally dangerous. Short put is also risky. Short put maximum loss = X - premium (bounded because a stock cannot fall below zero). Large, but not unlimited. Short CALL is unlimited because a stock's upside is uncapped.
Unit: pricing-and-valuation-of-options
Question 11Exam level
A call option is most likely said to be 'in-the-money' when:
How sure are you?
Correct: A. The correct answer is The stock price is above the exercise price. A call is in-the-money (ITM) when S > X. Exercising would produce a positive payoff of (S - X)..
B. If S equals X, the option is 'at-the-money'. A real and commonly tested definition that candidates confuse with ITM. S = X is at-the-money (ATM). In-the-money requires S strictly greater than X for calls.
C. Positive time value sounds like it should mean the option is in-the-money and worth exercising. All options before expiration have positive time value regardless of moneyness. An OTM option still has positive time value.
Unit: pricing-and-valuation-of-options
Question 12Harder
An at-the-money European call option and an at-the-money European put option on the same stock have the same expiration date and strike price. Which statement is most accurate regarding their time values when risk-free rates are positive?
How sure are you?
Correct: A. The correct answer is The call has greater time value than the put. For ATM options, intrinsic value = 0 for both, so option price equals time value. Due to the interest rate effect on the present value of the exercise price, the call has slightly higher time value when r > 0 (C > P for ATM options at positive rates, per put-call parity)..
B. Symmetry seems logical. Same stock, same strike, same expiry, ATM status. Why would they differ? The interest rate effect on the PV of the exercise price creates a slight value premium for calls over puts at positive rates.
C. ATM means intrinsic value = 0, and some candidates confuse this with time value also being zero. ATM options have zero INTRINSIC value but positive TIME value. Time value reflects the probability of finishing ITM. It is always positive before expiration.
Unit: pricing-and-valuation-of-options
Question 13Above the exam
Two otherwise identical call options on the same non-dividend-paying stock differ only in time to expiration: Option A expires in 3 months, Option B expires in 9 months. Combining the components of an option's value (intrinsic value plus time value) with how time to expiration affects time value, Option B's premium relative to Option A's should most likely be:
How sure are you?
Correct: B. An option's total value is intrinsic value plus time value. With the same strike and current stock price, both options have identical INTRINSIC value today, but Option B's longer time to expiration gives the underlying stock more opportunity to move favorably before expiration, which increases its TIME value component. All else equal, more time to expiration increases an option's premium (for standard American and most European options on non-dividend-paying stocks), so Option B should trade at a higher premium than Option A.
A. Longer time to expiration generally INCREASES, not decreases, an option's value, because it increases the time value component; claiming the opposite reverses one of the most basic relationships in option pricing.
C. Intrinsic value is only ONE of the two components of an option's premium; time value, which depends heavily on time to expiration (among other factors like volatility), is the other component, and it is exactly what differs between these two otherwise identical options.
Unit: pricing-and-valuation-of-options
Question 14Above the exam
A call option and a put option on the same stock share the same strike price and expiration date. The stock pays no dividends. Combining put-call parity with the specific effect of an increase in the risk-free interest rate, holding all else (stock price, strike, volatility, time) constant, an increase in the risk-free rate should most likely:
How sure are you?
Correct: A. Put-call parity (C + PV(X) = P + S) shows that the present value of the strike price is a key link between call and put values. A higher risk-free rate LOWERS the present value of the strike price (PV(X) falls); since S (stock price) is unchanged, and C + PV(X) = P + S must still hold, a lower PV(X) means C must rise relative to P (or equivalently, holding the relationship, a higher rate increases call values and decreases put values, since a call holder benefits from a cheaper effective strike price paid later, while a put holder's fixed future strike proceeds are worth less today).
B. The two options do not move in the same direction with a change in the risk-free rate; put-call parity shows they move in OPPOSITE directions as PV(X) changes, since the rate affects the present value of the fixed strike price differently for the right to BUY (call) versus the right to SELL (put) at that strike.
C. The risk-free rate is one of the recognized factors that determines option value (alongside stock price, strike, volatility, time, and dividends); put-call parity itself demonstrates the rate's role through the PV(X) term, so claiming no effect contradicts that basic relationship.