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xyrg+ · 2022年09月11日

英文看不懂

NO.PZ2017092702000095

问题如下:

A call option on a stock index is valued using a three-step binomial tree with an up move that equals 1.05 and a down move that equals 0.95. The current level of the index is $190, and the option exercise price is $200. If the option value is positive when the stock price exceeds the exercise price at expiration and $0 otherwise, the number of terminal nodes with a positive payoff is:

选项:

A.

one.

B.

two.

C.

three.

解释:

A is correct.

Only the top node value of $219.9488 exceeds $200

If the option value is positive when the stock price exceeds the exercise price at expiration and $0 otherwise。这句话是什么意思,在题中、对解题起到了怎样的作用?

1 个答案

星星_品职助教 · 2022年09月11日

同学你好,

这句话涉及到了后续衍生品科目里会学到的内容。

call option是看涨期权,即可以以固定的exercise price(执行价格)买入标的资产(本题中为股票)。如果此时标的资产的市价超过了exercise price,option的持有人就可以行权,以较低的exercise price价买入资产并赚钱。此时option value为正。

相反,如果标的资产市价低于了exercise price,option的持有人就不会行权,即不会用较高的exercise price去买入低价就可以从市场上买到的资产。此时option没有价值。

所以这句话可以理解为,当股票价格超过了exercise price的时候,option的价值就为正,否则就是0。

当optioin value为正(positive)时,就是positive payoff。由于已知exercise price为200,所以只需要计算出最后节点(terminal nodes)上四个值,找到超过200的就可以。即只有一个219.9488.

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