What is American vs European Options?

B is correct. Early exercise to capture the $3 dividend is advantageous here. By exercising today, Sarah buys 1,000 shares at $60 (total $60,000) when the market price is $85 (total $85,000), and the shares settle by the record date, so she receives the $3,000 dividend ($3 × 1,000 shares). After the ex-dividend date the stock drops to about $82, leaving her about $82,000 of stock plus the $3,000 dividend: $85,000 of value for $60,000, a $25,000 gain. If she holds the calls instead, the price drop cuts their intrinsic value to about $22 and they keep at most their $2 of time value, about $24,000. Exercising gives up $2,000 of time value to keep the $3,000 the dividend would otherwise strip from the calls, a net advantage of about $1,000. This is a classic American option advantage: early exercise before the ex-dividend date when the dividend exceeds the remaining time value.

A is incorrect because holding until expiration means missing the $3 dividend, which exceeds the $2 time value. After the ex-dividend date, the stock will drop to ~$82, reducing option value. C is incorrect because exercising on the ex-dividend date is too late: under T+1 settlement the ex-dividend date is the record date, so shares delivered the next business day carry no right to the dividend and have already dropped by about $3. D is nonsensical: you cannot convert option exercise styles. American vs European is determined at contract creation.

B is correct. This accurately defines the fundamental difference: American options provide the right to exercise at any time from purchase until the expiration date, while European options can only be exercised on the expiration date itself. This exercise timing flexibility is the sole distinction between the two styles and affects option valuation (American options typically cost more due to greater flexibility).

A is backwards: it reverses the definitions, incorrectly stating American options can only be exercised at expiration. C is incorrect because the names refer to exercise timing, not geographic location. European-style options trade on US exchanges (e.g., SPX index options are European-style but trade on US exchanges), and American-style options can trade anywhere. D is incorrect because both American and European options have standard expiration dates (typically the third Friday of the expiration month for equity options). The difference is when they can be exercised, not when they expire.

A is correct. The American option has every right of the otherwise identical European option plus the right to exercise early, so it is never worth less. Here that right has value: with a large dividend due before expiration, the American call holder can exercise just before the ex-dividend date and collect the dividend, while the European holder cannot. That justifies a premium for Option A. Without a dividend, early exercise of a call is never optimal, and the two calls would be worth the same.

B is backwards: greater rights (American) command higher prices, not lower. European options carry less assignment risk for sellers, because assignment can occur only at expiration, but that benefits the seller and adds no value for the buyer. C is incorrect because while both options have identical intrinsic value ($10 = $110 - $100), the American option's early exercise right has value when a dividend is due, making it worth more. D is incorrect because the gap between the two prices is the value of the early exercise right, not the amount of the expected dividends: the dividend lowers both calls, and early exercise recovers only the part of it that exceeds the time value given up.

C is correct (the exception). This statement is false. European options can be sold (closed) in the market before expiration at their current market value. They simply cannot be exercised early. The restriction is on exercise timing, not on trading or closing the position. An investor holding a European option can exit the position anytime by selling the option, realizing gains or losses based on current market price. Only the exercise feature is restricted to expiration.

A is accurate: American options provide the right to exercise at any point from purchase through the expiration date, offering maximum flexibility. B is accurate: European options restrict exercise to the expiration date only, with no early exercise permitted regardless of how profitable early exercise might be. D is accurate: most individual stock and ETF options traded on US exchanges (CBOE, NYSE) are American-style, while index options (like SPX, NDX) are typically European-style. This is an important distinction for practical option trading.

A is correct. Only statements 1 and 3 are accurate.

Statement 1 is true: the American option contains all rights of the European option plus early exercise capability, so it is never worth less and typically commands a higher premium. (For a call on a stock that pays no dividend before expiration, early exercise is never optimal and the two are worth the same.)

Statement 2 is false: European option sellers face assignment risk only at expiration, not anytime before. Since European options can only be exercised at expiration, sellers know exactly when assignment might occur. American option sellers face assignment risk at any time before expiration because buyers can exercise whenever they choose.

Statement 3 is true: Early exercise of American call options is most advantageous when a stock pays a dividend that exceeds the remaining time value of the option. By exercising early, the investor captures the dividend while forfeiting time value. If dividend > time value, early exercise is profitable. This is the classic dividend capture scenario and a key advantage of American options.

Statement 4 is false: Index options like SPX are typically European-style, not American-style. Most individual stock options are American-style, but major index options are European-style, exercisable only at expiration.