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real__yu · 2025年04月30日

这道题的答案是多少?

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).

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.

答案是多少

1 个答案

李坏_品职助教 · 2025年04月30日

嗨,从没放弃的小努力你好:


这个A节点的5.86就是答案,所以选D。


答案最后算出来,在A节点(也就是期初的时候)的期权价值是5.86,并且这个数字也大于期初的内在价值,所以期权在期初的合理价值就是5.86 USD。

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