Consider a portfolio that is delta neutral with gamma of 500

Consider a portfolio that is delta neutral, with gamma of -5,000 and a vega of -8,000. A traded option has a gamma of 0.5 and a vega of 2, and delta of 0.6. Second traded option with gamma of 0.8, vega of 1.2 and delat of 0.5. How could the portfolio be made delta, gamma, and vega neutral?

Solution

Delta, gamma and vega will be neutral or all equal to zero, when we\'ll adjust three parameters. This problem seem to imply that we are supposed to take a positions in the two new options . That lets us set two of these things to zero.

we are give gamma as = -5000

and the vega = -8000

We need to use the new options to set gamma and vega = 0

let x the amount of the first option that we buy

and let y be the amount of the second option that we buy

the first trade option has gamma = .5

and the second trade option has gamma = .8

=> [ .5x + .8*y ] - 5000 = 0

or .5x + .8*y = 5000 ----------(1)

he first trade option has vega = 2

and the second trade option has vega = 1.2

=> [ 2x + 1.2*y ] - 8000 = 0

2x + 1.2y = 8000 --------------(2)

from (1) and (2)

.5x + .8*y = 5000

2x + 1.2y = 8000

=> x = 400 and y = 6000