题目
A 1-year American put option with an exercise price of $40 will be worth $10.00 at maturity with a probability of 0.25 and $0.00 with a probability of 0.75. The current stock price is $36. The discount rate is 5%. The optimal strategy is to:
选项
A.Exercise the option because the payoff from exercise exceeds the present value of the expected future payoff.
B.Not exercise the option because the payoff from exercise is less than the discounted present value of the future payoff.
C.Exercise the option because it is currently at-the-money.
D.Not exercise the option because it is out-of-the-money.
答案
A
解析
The payoff from exercising the option is the exercise price minus the current stock price: $40﹣$36=$4.The discounted value of the expected future payoff is:「huixue_img/importSubject/1564169528047439872.png」It is optimal to exercise the option early because it is worth more exercised ($4.00) than if not exercised ($2.38).