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小熊猫 · 2023年05月01日

c为什么对？

  1. CFA I
  2. Derivative

NO.PZ2018062007000077

问题如下：

To determine the price of an option today, the binomial model requires:

选项：

A.

selling one put and buying one offsetting call.

B.

buying one unit of the underlying and selling one matching call.

C.

using the risk- free rate to determine the required number of units of the underlying.

解释：

C is correct. Pricing an option relies on the facts that a perfectly hedged investment earns the risk- free rate and that, based on the binomial option pricing model, the size of the two possible changes in the option price (meaning the potential step up or step down in the option value) after one period are equivalent.

中文解析：

本题考察的是用hedged portfolio 的方法对二叉树进行定价。注意V0 =hS0 -c0, 其中short call=long stock - long rf ，因为我们可以用long stock与short call相结合，构建出无风险组合。那么也可以用无风险组合与stock相结合，构造出short call。

中文解析只解释了选项a和b 但是没有讲c为什么对 以及 如何用risk free rate来determine units？

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1 个答案

pzqa27 · 2023年05月04日

嗨，从没放弃的小努力你好：


中文解析只解释了选项a和b 但是没有讲c为什么对

学术上一般都是证伪，几乎没有去证真的。C说的没有任何问题

如何用risk free rate来determine units？

如下图，C选项想表达整个定价的思路用到了rf，因为构建的组合期末payoff是确定的，那么投资者赚的是rf，所以risk free。只有买h份股票，卖1份call，才有一个确定的payoff，才有rf。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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