You hold a delta-neutral portfolio containing an undisclosed number of shares. It has a gamma of -5000 and a vega of -8000.

There are two traded options in the market:

Gamma Vega Delta

Option A 0.5 2.0 0.6

Option B 0.8 1.2 0.5

a)

What would you need to do to make the portfolio both vega and delta neutral?

What will be the new value of gamma?

b)

What would you need to do if you had to make the original portfolio both gamma, vega and delta neutral?