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一只可爱的猪 · 2020年03月02日

问一道题:NO.PZ2018062007000080

问题如下:

If a call option is priced higher than the binomial model predicts, investors can earn a return in excess of the risk- free rate by:

选项:

A.

investing at the risk- free rate, selling a call, and selling the underlying.

B.

borrowing at the risk- free rate, buying a call, and buying the underlying.

C.

borrowing at the risk- free rate, selling a call, and buying the underlying.

解释:

C is correct. If an option is trading above the value predicted by the binomial model, investors can engage in arbitrage by selling a call, buying shares of the underlying, and funding the transaction by borrowing at the risk- free rate. This will earn a return in excess of the risk- free rate.

这道题怎么考虑?用C+K=P+S吗

3 个答案

lynn_品职助教 · 2022年01月13日

嗨,努力学习的PZer你好:


讲的有点深了,BSM是二级才会考察的知识点~

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

lynn_品职助教 · 2021年12月15日

嗨,从没放弃的小努力你好:


这两个公式不能这么笼统的放在一起,BSM模型与put-call parity(C+K=P+S)是两种完全不同的定价模型。

首先平价公式的成立是有一些前提条件的,比如put 和call 有相同的执行价格,这个执行价格等于债券的面值,而BSM模型里面的C、K并没有这些前提条件,而BSM模型又有一些平价公式没有的假设。

具体见下图公式,在BSM里面,并不是C=S-K,K和S前面都有系数的,而平价公式里面S前面并没有系数。

我们通过BSM模型,提出括号里的负号,就可以得到long call = long stock + short bond,这不是完全等价的,只是可以这样操作。

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努力的时光都是限量版,加油!

𝒜𝒩𝒥𝒜 安雅🎃 · 2022年01月13日

BSM公式没有出现在讲义上呢(😓担心)不知道是不是我漏了啥?

xiaowan_品职助教 · 2020年03月02日

嗨,爱思考的PZer你好:


同学你好,这里不是用平价公式来分析的。在二叉树定价模型下,我们认为call被高估了,那么就要short call,同时long一份复制的call,而选项中borrowing at the risk-free rate and buying the underlying,也就是借钱买股票就可以复制出一个call,这样我们可以通过卖出一个被高估的call,买入一个合理定价的call来获利。


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加油吧,让我们一起遇见更好的自己!


李梦璐 · 2021年12月15日

老师,这里我有跟点C+K=P+S弄混了,long一份复制的call,那根据C+K=P+S不是需要里面有个put option才能相等么?为何orrowing at the risk-free rate and buying the underlying就可以等价于一个long call了?

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