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甜甜 · 2024年06月03日

exercise value

NO.PZ2016031201000037

问题如下:

For a European call option with two months until expiration, if the spot price is below the exercise price, the call option will most likely have:

选项:

A.

zero time value.

B.

positive time value.

C.

positive exercise value.

解释:

B is correct.

A European call option with two months until expiration will typically have positive time value, where time value reflects the value of the uncertainty that arises from the volatility in the underlying. The call option has a zero exercise value if the spot price is below the exercise price. The exercise value of a European call option is Max(0, StXS_t-X ), where StS_t is the current spot price at time t and X is the exercise price.

中文解释:

距离到期日还有两个月的欧式看涨期权具有正的时间价值。B正确。

现货价格低于执行价格,看涨期权的执行价值为零。欧式看涨期权的行权值为Max(0,St -X)。

exercise value不是ST-X(1+r)^-(T-t)吗?那万一X折到T时间点小于ST了那exercise value会大于0吗?

2 个答案

李坏_品职助教 · 2024年06月04日

嗨,从没放弃的小努力你好:


St - X*(1+r)^(T-t)如果大于0,那就是exercise value  = St - X*(1+r)^(T-t) , 大于0。


但这道题说的是“ if the spot price is below the exercise price”,已经限制条件为St小于X了,所以本题的exercise value = 0.

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努力的时光都是限量版,加油!

李坏_品职助教 · 2024年06月03日

嗨,努力学习的PZer你好:


题目条件已经告诉我们“with two months until expiration”, “if the spot price is below the exercise price, ”


意思是现在的时间就是距离到期日还有2个月,当前的S小于X。问你在这些条件限定下,call option当前的value是怎样的?你不需要考虑到期日的问题。


在任何时刻,call option的exercise value = max(0, 当前的现货价格St - X*(1+r)^(T-t))。

当前还没到期,所以time value大于零。由于现货价格S小于执行价格X,所以看涨期权当前的exercise value = 0.



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努力的时光都是限量版,加油!

甜甜 · 2024年06月04日

在任何时刻,call option的exercise value = max(0, 当前的现货价格St - X*(1+r)^(T-t))。St - X*(1+r)^(T-t)万一大于0咋办?

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