题目
A market maker writes (sells) a contract of 100 call options, where the percentage (per option) delta of the call options is 0.60 and the gamma is 0.080. The market maker wants to neutralize both the delta and gamma of this position (delta-gamma-neutral) with two additional trades: the underlying shares; and put options on the stock with percentage delta of -0.40 and gamma of 0.020. What are the trades?
选项
A.Buy 200 put options and buy 80 shares
B.Sell 200 put options and sell 80 shares
C.Buy 400 put options and buy 220 shares
D.Sell 400 put options and sell 220 shares
答案
C
解析
The written options have position delta = -100 × 0.60 = -60.0; and position gamma of -100 × 0.080 = -8.0.The puts must be used to neutralize the position (as the shares have zero gamma).As 8.0/0.020 = 400, 400 put options must be purchased to neutralize gamma: +400 × 0.020 = +8.0 which neutralizes the -8.0.But the long 400 put options reduced (added negative) position delta = +400×-0.40=-160.0such that the cumulative position delta = -60.0 +-160.0 = -220.0.Therefore, the market maker must purchase 220 shares (with +1.0 delta each) to neutralize delta.To summarize, the final position:Delta=(-100× 0.60)+(+400×-0.40)+(220×1.0)=0; andGamma=(-100×0.080)+(+400×0.020)+(220×0)=0.为了使投资组合的gamma 300达到gamma中性， 卖出300/0.12=2,500的看涨期权 卖出期权的delta= -100 × 0.60 = -60.0；gamma为-100 × 0.080 = -8.0.看跌期权被认为要达到中性。8.0/0.020 = 400, 买入400份看跌期权可以达到gamma中性 400 × 0.020 = 8.0（与-8.0中和）。但是买入400份看跌期权减少了delta= 400×－0.40=－160.0现在累计的delta= －60.0 ＋160.0 = －220.0.因此做市商需要都卖220份股票来达到delta中性，此时的delta和gamma都为0.