NO.PZ2023091802000133
问题如下:
An analyst is pricing a 2-year European put option on a non-dividend-paying stock using a binomial tree with two time steps of one year each. The stock price is currently USD 38, and the strike price of the put is USD 40. Assuming that the annual risk-free rate will remain constant at 2% over the next two years and the annual stock volatility is 15%。The risk neutral probability of an up move is 57.61% (calculated in the previous question).
The no-arbitrage price of the option is closest to:
选项:
A.USD 2.00
B.USD 2.93
C.USD 5.22
D.USD 5.86
解释:
The risk neutral probability of an up move is 57.61% (calculated in the previous question).
Node B: (0.5761 × 0 + 0.4239 × 4) × exp(-0.12
× 3/12) = 1.65, which is greater than the intrinsic value of the option at this
node equal to max(0, 52 – 60) = 0, so the option should not be exercised early
at this node.
Node C: (0.5761 × 4 + 0.4239 × 20) × exp(-0.12
× 3/12) = 10.46, which is lower than the intrinsic value of the option at this
node equal to max(0, 52 – 40) = 12, so the option should be exercised early at
node C, and the value of the option at node C is 12.
Node A: (0.5761 × 1.65 + 0.4239 × 12) ×
exp(-0.12 × 3/12) = 5.86, which is greater than the intrinsic value of the
option at this node equal to max(0, 52 – 50) = 2, so the option should not be
exercised early at this node.
答案是多少