You have a delta neutral portfolio and the following information:

Delta Gamma Vega

Portfolio 0 -5000 -8000

Option 1 0.6 0.5 2.0

Option 2 0.5 0.8 1.2

a) What position in option 1 and the underlying asset will make the portfolio delta and gamma neutral?

b) What position in option 1 and the underlying asset will make the portfolio delta and vega neutral?

c) What position in option 1, option 2, and the asset will make the portfolio delta, gamma, and vega neutral?

There is no other information.