题目
An at-the-money call option has a (percentage) delta of 0.600 and gamma of 0.030. A market maker writes (sells) 100 call options, but only after the stock price unexpectedly jumps $2.00, so the written options are immediately in-the-money by $2.00. How many shares should the market maker buy to neutralize the delta of the option position?
选项
A.Long 3.0 shares
B.Long 60.0 shares
C.Long 63.0 shares
D.Long 66.0 shares
答案
D
解析
Gamma is the change in delta given a change in the stock price, such that if the stock price increases by $2.00, we expect the "percentage delta" to increase by 2.00×0.030=0.060 to 0.660; i.e., new delta =0.60+(2×0.030) = 0.660. The position delta is therefore -100×0.660=-66, such that 66 shares are purchased to neutralize delta.Gamma是给定股价变化后的增量变化，因此，如果股价上涨2.00美元，我们预计“百分比变化率”将增加2.00×0.030 = 0.060至0.660； 即新增量= 0.60＋（2×0.030）= 0.660。 因此，头寸delta为-100×0.660 = -66，因此购买了66股股份以达到delta中性。