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阿萌酱 · 2020年08月12日

问一道题: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.

这道题的考点怎么理解呢

1 个答案

袁园_品职助教 · 2020年08月12日

同学你好!

这道题考的是delta对冲。

delta对冲就是无论现货S价格怎么变,资产组合的价格变化都为0。也就是说,应该令资产组合的价格P ,对现货S的导函数为0 (严格来说是偏导数),最后把n求出来和100相乘,就是现货数量。差的值,就通过买入或卖出来调整。

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