题目
A portfolio has the following position Greeks: delta = -300, gamma = -150, and vega = - 3,000. A trader wants to neutralize all three Greeks and, in addition to the underlying shares, can use the following two options: Call option with the following percentage Greeks: delta = 0.60, gamma = 0.20, and vega = 10.0 Put option with the following percentage Greeks: delta = -0.40, gamma = 0.30, and vega = 20.0 Along with the underling shares, which set of trades will make the total position delta-gamma-vega neutral?
选项
A.Short 800 of the calls; long 150 of the puts, and short 500 of the underlying shares
B.Short 1,500 of the calls; short 680 of the puts, and long 770 of the underlying shares
C.Long 2,100 of the calls; short 900 of the puts; and short 1,320 of the underlying shares
D.Long 3,000 of the calls; short 1,750 of the puts; and long 540 of the underlying shares
答案
C
解析
Let x = number of call options and y = number of put options. Gamma and vega neutrality are implied by:Gamma neutral: -150 + 0.20x + 0.30y=0 -->0.20x + 0.30y = 150, andVega neutrals: -3,000 + 10x + 20y = 0 --> 10x + 20y = 3,000.This is two equations and two unknowns such that x = 2,100 and y = -900.The delta of this gamma-vega neutral portfolio = -300 + 2100×0.60 - 900×(-0.40) = 1,320 such that short 1,320 will neutralize delta. 设x =看涨期权数量，y =看跌期权数量。若满足gamma中性和vega中性：Gamma neutral: －150 ＋0.20x ＋0.30y=0 0.20x＋0.30y = 150, Vega neutrals: －3,000＋10x ＋20y = 0 10x＋20y = 3,000.可以得到x=2100，y=-900这个gamma和vega中性的资产组合的delta为= －300 2100×0.60 －900×(－0.40) = 1,320。则再卖1320份股票达到delta中性