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Anna · 2024年11月01日

为什么equity call option的delta是近似于1?

NO.PZ2023041003000056

问题如下:

Toye asks Malarkey to provide insight on the relationship between the price of a Lipton call option and the underlying stock. Malarkey states that for any equity call option, delta will be approximately 1.0 and gamma will tend to be large whenever the option is in the money as it nears maturity.

Are Malarkey’s explanations of delta and gamma for in-the-money call options most likely correct?

选项:

A.

No, he is incorrect about the gamma measure

B.

No, he is incorrect about the delta measure

C.

Yes

解释:

Gamma is a measure of the sensitivity of delta to a change in the stock price. Gamma is largest for options that are at the money near maturity because of the uncertainty about whether the option will expire (1) in the money (delta is 1.0) or (2) out of the money (delta is 0.0).

Gamma的原因可以理解,不太理解为什么call option on equity的结论

1 个答案
已采纳答案

李坏_品职助教 · 2024年11月01日

嗨,爱思考的PZer你好:


后面有个条件句“whenever the option is in the money as it nears maturity.”。意思是当期权是实值期权,并且临近到期日的时候。

先来看BSM模型:

delta of C = dC / dS = N(d1)。call option的delta就是N(d1),这是正态分布累积概率函数。


当临近到期日时,T近似于0,那么d1的分母近似于0。又因为是in the money call,所以S大于K,所以分子是大于0的,那么d1是无穷大的。

一个无穷大的变量的正态分布累积概率约等于100%,N(d1)≈1。

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