1. Assume that you have an option portfolio with delta 10 and vega 200, and you want to alter your delta and vega exposure using two liquid contracts. The first contract has a delta of 0.5 and vega of 2. The second contract has delta of zero and vega of 6.

   (a) How many of these two contracts do you need in order to balance your portfolio to delta and vega neutral? (b) Suppose you want to achieve delta neutral but are willing to have a vega exposure within 10. What are the minimum number of contracts you need to get your portfolio within your target exposure range?