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Kitty · 2025年04月01日

不理解

NO.PZ2023040401000072

问题如下:

A European call option and a European put option are written on the same underlying, and both options have the same expiration date and exercise price. At expiration, it is possible that both options will have:

选项:

A.

negative values.

B.

the same value.

C.

positive values.

解释:

B is correct. If the underlying has a value equal to the exercise price at expiration, both options will have zero value since they both have the same exercise price. For example, if the exercise price is $25 and at expiration the underlying price is $25, both the call option and the put option will have a value of zero. The value of an option cannot fall below zero. The holder of an option is not obligated to exercise the option; therefore, the options each have a minimum value of zero. If the call has a positive value, the put, by definition, must have a zero value and vice versa. Both cannot have a positive value.

老师可以讲一下这道题为什么是same吗,感觉没太理解题的意思

1 个答案

李坏_品职助教 · 2025年04月01日

嗨,努力学习的PZer你好:


首先,期权的总价值 = 时间价值+内在价值。因为本题是At expiration(已经在到期日了),所以时间价值为0,只剩下内在价值。


看涨期权的内在价值 = max(S-K , 0),看跌期权的内在价值=Max(K-S, 0),无论怎样,内在价值都是大于等于0的。当S-K = K-S = 0的时候,看涨期权与看跌期权才有可能出现价值相同的情况,也就是他们的价值都是zero,此时call and put options have the same value.

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