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ruby5ltc · 2022年05月28日

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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。

为什么要short call 就要同时long一份复制的call?

为什么borrowing at the risk-free rate and buying the underlying是借钱买股票的意思?

借钱买股票怎么复制出一个call呢?

1 个答案

Lucky_品职助教 · 2022年05月29日

嗨,努力学习的PZer你好:


1、因为earn a return in excess of the risk- free rate说明了是无风险套利,也就是arbitrage,发现并利用市场定价不合理获取利润

2、borrowing at the risk-free rate是借钱的意思,buying the underlying是买标的物也就是股票的意思

3、call=max(0.St-X/(1+r)^t] ,根据公式可以看出,call的收益类似借钱买股票,St是买股票,-X/(1+r)^t是借钱

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