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Pavel Korchagin · 2023年07月01日

C为什么对?

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。

之前别的同学的问题里面的回答没看懂是什么意思,题目说要决定hedge的unit number是多少,这不是hedge ration公式用Δp和Δs算出来的吗?和rf有什么关系???

1 个答案

Lucky_品职助教 · 2023年07月02日

嗨,爱思考的PZer你好:


这个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。只有买h份股票,卖1份call,才有一个确定的payoff,才有rf。但这个选项的阐述方法不是很严谨。


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