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摩羯大小姐 · 2022年01月15日

知道要short call 怎么从公式推导出答案

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.

中文解析:

在二叉树定价模型下,现在认为call被高估了,那么就要short call,同时long一份复制的call。低买高卖进行套利。

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。

知道要short call 怎么从short call=long stock+short bond推导出答案?
3 个答案
已采纳答案

lynn_品职助教 · 2022年01月15日

嗨,努力学习的PZer你好:


这道题的思路是这样的,知道要short call,因为要空手套利,所以就需要再long call的复制品,在二叉树定价模型下,long call = long stock+short bond,所以我们的头寸是,short call + long stock + short bond;long stock 等于 buying underlying,short bond 等于 borrowing money,所以选C。

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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!

摩羯大小姐 · 2022年02月02日

我笔记里记得是short call=long stock+short bond,看答案等式左边是long call 是我的笔记记错了是吗

𝒜𝒩𝒥𝒜 安雅🎃 · 2022年02月06日

我也有和摩羯大小姐同学相同的疑问,求老师解答。

Lucky_品职助教 · 2022年08月04日

嗨,努力学习的PZer你好:


回复Leo 昊子:

我又思考了一下,我觉得用期权平价公式没那么严谨,应该是二叉树原理~ 二叉树模型是在假设标的资产在未来一期有上涨下跌两种情况的前提下,对期权进行估值的一种方法。

这个call是通过二叉树原理构建出来的,在完美对冲的情况下,long stock + short call = rf (获得无风险收益), 获取rf 其实是long bond,挪一下项就是long call = long stock+short bond

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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!

Lucky_品职助教 · 2022年02月11日

嗨,努力学习的PZer你好:


根据期权平价公式C+K=P+S来考虑,call overvalued,也就是市场的call被高估了,你自己估值算的call并不值这么多,你认为将来价格会下跌,那就应该short 市场call(现在卖call,将来价格跌了再买回来,这样就赚了差价)。

为了获利(建立一个反向头寸),我们要用现货买入合成的call(也就是自己估算的理论的call),根据期权平价公式C+K=P+S,C=s-k+p,我们可以看出用long s(stock)(即buying the underlying) , short k(bond)(即borrowing at the risk- free rate发债融资/借钱)来合成call。

short市场的高估的call,long通过理论合成的价值公允的call,就可以赚取自己发现的利润,就是答案C所描述的。

你的笔记有误,你把short 市场call和long合成的call混在一起了~

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努力的时光都是限量版,加油!

Leo 昊子 · 2022年08月04日

,C=s-k+p,p在答案里没有体现啊

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