Questions: Call and Put Options: Rights, Exercise, and Payoffs

Question 1

You hold an American call option on a stock with strike K = $60. The stock currently trades at $75. A friend says 'Exercise now and lock in your $15 profit before the price drops.' What is wrong with this advice?

• A. Nothing — exercising immediately is always optimal for in-the-money American calls
• B. Early exercise sacrifices the option's time value; the option is worth more than $15 alive, so selling it in the market dominates early exercise
• C. You cannot exercise an American call when the stock is above the strike price
• D. The $15 gain is not real profit until you separately sell the acquired shares

Answer: (B)

An in-the-money option has both intrinsic value ($15 = S − K) and time value. Early exercise captures only the intrinsic value and forfeits the time value. For a non-dividend-paying stock, it is almost never optimal to exercise an American call early — you are better off selling the option itself for more than $15. The friend's advice treats the option as if it were the stock, ignoring the option's remaining optionality.

Question 2

You buy a put option with strike K = $40 for a premium of $3. At expiration, the stock is at $35. What is your net profit per share?

• A. −$3 (the option expires worthless)
• B. +$2 (put payoff of $5 minus $3 premium)
• C. +$5 (the full put payoff)
• D. −$5 (you are obligated to sell at $40)

Answer: (B)

Put payoff = max(K − S, 0) = max(40 − 35, 0) = $5. You exercise because K > S. Net profit = $5 payoff − $3 premium = $2. Option A is wrong because S < K so the put is in-the-money and will be exercised. Option D reflects the fundamental misconception that options create obligations — the put buyer has a RIGHT to sell, not an obligation.

Question 3

A put option becomes more valuable as the underlying stock price rises.

• T. True
• F. False

Answer: False

Put payoff = max(K − S, 0). As S rises above K, the payoff goes to zero — the put moves out of the money and loses value. Puts are bearish instruments that profit when the stock falls below the strike price. Calls increase in value when the stock rises; puts increase in value when the stock falls.

Question 4

The maximum loss for the buyer of a call option is limited to the premium paid, regardless of what happens to the underlying stock price.

• T. True
• F. False

Answer: True

The call buyer holds a RIGHT but not an OBLIGATION to buy. If the stock falls below the strike at expiration, they simply don't exercise — the option expires worthless, and the loss is exactly the premium paid, nothing more. This is the asymmetry that defines options: the buyer's downside is capped at the premium while the upside is theoretically unlimited (for calls) or large (for puts).

Question 5

Why is the 'right but not obligation' feature of options fundamental to understanding their payoff structure? How does it create the asymmetric risk profiles for buyers versus sellers?

Model answer: Holders exercise only when it benefits them — when S > K for calls or K > S for puts — so the payoff is never negative: max(S − K, 0) and max(K − S, 0). This means buyers face limited downside (premium paid) and potentially large upside. Sellers take the opposite side: they collect the premium but face the buyer's upside as their potential loss. For call sellers, this loss is theoretically unlimited as S can rise without bound. This zero-sum asymmetry at expiration is what makes options useful for hedging: one party transfers risk and pays a premium; the other bears the risk in exchange for the premium.

The right-not-obligation structure is what distinguishes options from futures or forward contracts, where both parties have obligations. It is precisely this optionality that gives options their characteristic payoff shape and makes them powerful but also often misunderstood.