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蜗牛也是牛Megan · 2025年05月04日

怎么计算

NO.PZ2025040202000032

问题如下:

A trader sells a put option on 10,000 shares of a stock. The option call delta is 0.612 and the option put delta is –0.363. Assuming the hedging instrument is stock, the appropriate delta hedge is executed by which of the following transactions?

选项:

A.A.Buy 3,630 shares of stock B.B.Short sell 3,630 shares of stock C.C.Short sell 6,120 shares of stock

解释:

A Incorrect because the trader sells, not buys, the put option. Therefore, the trader must sell, not buy, the underlying to achieve a delta neutral portfolio.

B Correct because the put delta is given as –0.363, thus the short put delta is 0.363, and the number of number of hedging units is NH = – Portfolio delta / DeltaH = – (3,630 / 1) = –3,630 or short sell 3,630 shares of stock, where Portfolio delta = 10,000 (0.363) = 3,630 and DeltaH = 1.0. Delta hedging an option is the process of establishing a position in the underlying stock of a quantity that is prescribed by the option delta so as to have no exposure to very small moves up or down in the stock price. Let NH denote the number of units of the hedging instrument and DeltaH denote the delta of the hedging instrument, which could be the underlying stock. Delta neutral implies the portfolio delta plus NHDeltaH is equal to zero. The optimal number of hedging units, NH, is NH = Portfolio delta / DeltaH. Note that if NH is negative, then one must short the hedging instrument, and if NH is positive, then one must go long the hedging instrument.

C Incorrect because this uses the call delta rather than the put delta.

这里按照老师给的公式,不考虑正负号的话,算出来Ns=3630,不就是应该买入股票吗?

1 个答案

李坏_品职助教 · 2025年05月04日

嗨,从没放弃的小努力你好:


这个人是sell put,就是卖出看跌期权。想一下卖出看跌期权的payoff图像,是在股价下跌的时候会亏钱。


为了对冲这个风险,我们必须找到一种办法,能够在股票下跌时有利润,这样才能对冲上面的sell put的风险。 能实现这个目的的交易方式,就是short stock。所以应该是Short 而不是买入股票。

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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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