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J · 2020年07月21日

问一道题：NO.PZ2018062007000080 [ CFA I ]

  1. CFA I
  2. Derivative

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.

请问这个call是怎么模拟出来的？long stock short bond没法模拟call不行权的那部分啊？
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1 个答案

xiaowan_品职助教 · 2020年07月22日

嗨，努力学习的PZer你好：


同学你好，

这个call是通过二叉树原理构建出来的，就如李老师课程中所讲解的，一阶段二叉树的定价原理就是构建-c+hS的组合，

令T时刻，-(c-)+h(S-)=-(c+)+h(S+)，然后推导出c=hS+PV(-h(S-)+(c-))=hS+PV(-h(S+)+(c+))，也就是long stock+short bond，

通过这个过程我们可以看到，这个replication保证的是0时刻组合和T时刻组合的价值相等，而不是从0到T整个轨迹的payoff形态相同。


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