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小壹万万呀 · 2022年08月04日

请问是这样理解这道题目吗？

  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.

  1. 是用这个non-dividend-paying stock来对冲这个 short call
  2. 现在需要对冲100 share，所以需要买0.5*100 = 50 share
  3. 将来delta变化，只需要0.44*100 = 44 share


如果是用ΔP = ΔB + ΔH = 0 这个原理去理解，这道题应该怎么算啊？

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2 个答案

李坏_品职助教 · 2022年08月05日

嗨，努力学习的PZer你好：


sorry我写错了，应该是股票价格从100跌到了99，对应的call的delta从0.5变成了0.44.由于是short call，所以delta是从-0.5变成了-0.44。

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李坏_品职助教 · 2022年08月04日

嗨，从没放弃的小努力你好：


你理解的是对的。


股票价格是从50跌到44，所以short call option的delta的变化值△B =[(-0.44)-(-0.5)]* 100 = 6。

为了让△P= 0，要让△H = -6。这里的hedge的工具就是stock，而stock的delta = 1，所以需要△H / 1 = -6 这么多股票来对冲short call。就是sell 6 shares。

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小壹万万呀 · 2022年08月04日

股票价格不是从100 跌到99吗?

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