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ruby5ltc · 2023年07月09日

请问

  1. CFA II
  2. Derivative

NO.PZ2023020101000023

问题如下：

Cummins states that long-/short-hedge fund managers seek to identify and exploit any mispricing that may exist between the price of an option and the price of its underlying stock, utilizing a replicating strategy. Cummins asks Spelding to assess the three scenarios outlined in Exhibit 2, based on the information in Exhibit 1 and assuming that the price of a one-year European-style call option is $19.25.

Exhibit 1: Binomial Model Variables and Values

Exhibit 2: Scenarios and Replicating Strategies

With respect to the replicating strategies, which scenario is most likely correct:

选项：

A.

Scenario 1.

B.

Scenario 2.

C.

Scenario 3.

解释：

The $19.25 price of the call option exceeds its value of $15.44, as calculated based on both the no-arbitrage approach and the expectations approach. Accordingly, the replicating strategy per 100 shares is to (1) sell 1 option, (2) buy h shares, and (3) borrow h * (up/down factor price + up/down call payoff).

The call option calculations follow:

• No-arbitrage approach:

Hedge ratio

h=c+−c−S+−S−=35−0135−75=3560=0.5833h=\frac{c^+-c^-}{S^+-S^-}=\frac{35-0}{135-75}=\frac{35}{60}=0.5833

Call Option value

c=hS+PV(−hS−+c−=0.5833∗100+(−75∗0.5833)1.02+0=$15.44c=hS+PV(-hS^-+c^-=0.5833\ast100+\frac{{(-75\ast0}{.5833)}}{1.02}+0=\$15.44

• Expectations approach:

Probability of an up move π=0.45

Call Option value

c=35∗0.45+01+0.2=$15.44c=\frac{35\ast0.45+0}{1+0.2}=\$15.44

Accordingly, the replicating strategy per 100 shares is to (1) sell 1 option, (2) buy h shares, and (3) borrow h * (up/down factor price + up/down call payoff).

算出来的15,44我懂，怎么操作我没理解

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2 个答案

pzqa27 · 2023年07月13日

嗨，爱思考的PZer你好：


题目并未给出put option以及bond的相关信息，因此条件不够

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

pzqa27 · 2023年07月12日

嗨，从没放弃的小努力你好：


这个题告诉我们一个call现在卖19.25美金，然后给出了目前的股价，执行价格等一系列信息，问我们怎么进行套利。

我们先算一算这个call 理论上值多少钱，解析算了后发现是15.44美金，现在一个本来值15.44美金的call，却在市场上卖19.25，那么就可以进行套利。

这里根据题目选项，可以发现我们是通过股票和期权来构建套利组合。

根据套利的基本原理，我们需要买入被低估的，卖出被高估的。目前这个call肯定是被高估了，所以卖出1份call。又根据无套利组合，每卖出1份call，需要long Δ份股票，因此我们long0.58份股票，然后我们算一算发现，short call 可以赚19.25, long 0.58份股票需要花58元，因此根据套利不花自己一分钱的原则，需要借钱。所以总结下来就是 short call，long stock,同时借钱。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

ruby5ltc · 2023年07月12日

可以用P+S=C+K解释吗

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2024-09-05 22:02 1 · 回答

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