题目
Robert the Trader has already written 1,000 call options with (percentage) delta of 0.670 and gamma of 0.090 such that his position delta is -670.0 and his position gamma is -90.0. He can buy or sell another call option on the stock; this additional call option has (percentage) delta of 0.560 and gamma of 0.150. Which trade will neutralize delta and gamma?
选项
A.Buy 600 call options and buy 334 of the underlying shares
B.Buy 400 call options and sell 215 of the underlying shares
C.Sell 300 call options and buy 180 of the underlying shares
D.Sell 260 call options and sell 155 of the underlying shares
答案
A
解析
First, he can neutralize gamma with -(-90)/0.15 = long +600 options; then, total gamma = -90×(+600×0.15) = 0.But delta = -670 + (+600×0.560) =－334.0 such that long 334 shares are required to neutralize delta (and these shares do not impact gamma as the percentage gamma of shares is zero).首先，使gamma中性：-(-90)/0.15 = 600， 买入600份期权，然后，总gamma= －90×( 600×0.15) = 0.而delta= －670＋ ( 600×0.560)=－334.0，则买入334份股票可以达到delta中性（股票的gamma为0，不会影响总gamma）。