怎么计算

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 N_H = – Portfolio delta / Delta_H = – (3,630 / 1) = –3,630 or short sell 3,630 shares of stock, where Portfolio delta = 10,000 (0.363) = 3,630 and Delta_H = 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 N_H denote the number of units of the hedging instrument and Delta_H denote the delta of the hedging instrument, which could be the underlying stock. Delta neutral implies the portfolio delta plus N_HDelta_H is equal to zero. The optimal number of hedging units, N_H, is N_H = − Portfolio delta / Delta_H. Note that if N_H is negative, then one must short the hedging instrument, and if N_H is positive, then one must go long the hedging instrument.

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