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0.030x + 0.020y =0 (gamma neutrality)
0.180x + 0.150y =-10 (Vega risk)
0.030x=-0.020y
x=-0.020y/0.030 =-.667y
substitute x i (vega risk formula)
0.180(-.667y) + 0.150y=-10
-.120y + 0.150y=-10
0.03y=-10
y= -10/0.03 = - 333.33
now solve for x
0.030x= - 0.020y
0.030x=-0.020(-333.33)
x=-0.020(-333.33)/0.030
x=222.22
ok ?
good luck
mike
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