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wzhen2017 · 2022年02月01日

可否提供一下这个题目计算对冲用到的等式

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2016070202000027

问题如下：

A non-dividend-paying stock has a current price of $100 per share. You have just sold a six-month European call option contract on 100 shares of this stock at a strike price of $101 per share. You want to implement a dynamic delta-hedging scheme to hedge the risk of having sold the option. The option has a delta of 0.50. You believe that delta would fall to 0.44 if the stock price falls to $99 per share. Identify what action you should take now (i.e., when you have just written the option contract) to make your position delta- neutral. After the option is written, if the stock price falls to $99 per share, identify what action should be taken at that time (i.e., later) to rebalance your delta-hedged position.

选项：

A.

Now: buy 50 shares of stock; later: buy 6 shares of stock.

B.

Now: buy 50 shares of stock; later: sell 6 shares of stock.

C.

Now: sell 50 shares of stock; later: buy 6 shares of stock.

D.

Now: sell 50 shares of stock; later: sell 6 shares of stock.

解释：

The answer is B.

The dynamic hedge should replicate a long position in the call. Due to the positive delta, this implies a long position of Δ×100=50 shares. If the delta falls, the position needs to be adjusted by selling   (0.5−0.44)×100=6\;{(0.5-0.44)}\times100=6 shares.

请问老师，可否提供一下这个题目计算对冲用到的等式，大概是 原来的=n份*对冲后的。有些想不明白计算的过程，谢谢。

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DD仔_品职助教 · 2022年02月03日

嗨，从没放弃的小努力你好：


同学你好，

这道题delta发生了变化，我们只需要一个公式来判断delta变化前后的股票数的差别，即可计算出答案。

所需股票数=delta*期货数量

目前的头寸是short了100个call，做对冲就需要long stock

delta是0.5时，所需的股票数就是0.5*100=50个，long50个stock

delta是0.44时，所需的股票数就是0.44*100=44个，原本是50个，现在只需要44个，那就卖出6个股票即可。

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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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