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?