Problem 28. A stock doesn't have any ex-dividend date in the next three months. The volatility of the stock price is 20%, and the interest rate is 2%. Which of the following is most likely correct? (a) The delta of a 3-month ATM call on the stock is 0.4602. (b) The delta of a 3-month ATM put on the stock is 0.5398. (c) The delta of a 3-month ATM put on the stock is -0.4602. (d) The delta of a 3-month ATM call on the stock is -0.5398. Problem 24. Assume all the Black-Scholes assumptions hold for stock price XYZ. The interest rate is 0%. A European gap call option on the stock has a strike price of 45 and a gap of 5. The option will mature in three months from today. The stock price is $50 today, and its volatility is 40%. The risk-neutral probability that the gap option pays at least $5 in three months is (a) exactly 0%. (b) exactly 50%. (c) more than 50%. (d) less than 50%. Problem 28. A stock doesn't have any ex-dividend date in the next three months. The volatility of the stock price is 20%, and the interest rate is 2%. Which of the following is most likely correct? (a) The delta of a 3-month ATM call on the stock is 0.4602. (b) The delta of a 3-month ATM put on the stock is 0.5398. (c) The delta of a 3-month ATM put on the stock is -0.4602. (d) The delta of a 3-month ATM call on the stock is -0.5398. Problem 24. Assume all the Black-Scholes assumptions hold for stock price XYZ. The interest rate is 0%. A European gap call option on the stock has a strike price of 45 and a gap of 5. The option will mature in three months from today. The stock price is $50 today, and its volatility is 40%. The risk-neutral probability that the gap option pays at least $5 in three months is (a) exactly 0%. (b) exactly 50%. (c) more than 50%. (d) less than 50%