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a1132766866 · 2023年09月23日

公式

  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。

所以无论是long call 还是short call,都等于long stock +short rf 吗？

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1 个答案

pzqa35 · 2023年09月25日

嗨，努力学习的PZer你好：


这道题的解析是存在问题的，应该是long call=long stock +short rf，call option在到期的收益率是ST-X，所以期初需要借入X/(1+rf)T，同时买入股票S0，期末之后卖出股票获得ST的收益，同时还借款X，现金流即为ST-X。老师在基础班也讲过该知识点：

所以long call=long stock +short rf，short call=long rf + short stock，我们已经在后台进行了修改，同学能够发现问题，说明此知识点的掌握情况非常扎实哦。

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