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410140980 · 2023年07月01日

option的number

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.

老师这句话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.当中是理解为期权的数量是100呢还是100*100? 有的时候看题目是要一份期权对应n份股票,所以期权的总数就是100*100,有时候就直接是期权的数量。表述上有没有固定的搭配?

1 个答案

DD仔_品职助教 · 2023年07月01日

嗨,从没放弃的小努力你好:


同学你好,

这句话说的是你刚卖了一个call option,这个call option涵盖了100只股票,期权数=1,股票数=100。

一份期权对应n个股票,那么期权总数就是1呀,怎么能说100*100呢。

这个表述就是题目字面的意思呀,固定搭配也就是a option对应几个股票

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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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