这题没有给条件

问题如下：

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).

The figure shows the stock price and the respective option value at each node. At the final nodes the value is calculated as max (0, K – S).

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.