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lynn666 · 2023年02月04日

关于买卖方向的问题

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   (0.50.44)×100=6\;{(0.5-0.44)}\times100=6 shares.

这里因为题目中说的是just sold call option所以为了对冲 now 需要 buy stock。是这样理解的吗?

1 个答案
已采纳答案

pzqa27 · 2023年02月05日

嗨,努力学习的PZer你好:


嗯,是的,题目说现在卖出了100份的call,如果要现在就Δ neutral ,只能买入50份的股票,过了一段时间后Δ变成0.44了,此时需要neutral只需要44份股票即可中性了,而手上有50份股票,所以卖掉6份就好了

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