A financial institution has the following portfolio of over-the-counter options on IBM: Type Position Delta of Option Gamma of Option Vega of Option Call -1,000 0.5 2.2 1.8 Call -500 0.8 0.6 0.2 Put -2,000 -0.4 1.3 0.7 Call -500 0.7 1.8 1.4 A traded options not in the above portfolio on IBM are available with: Option 1: delta = 0.6, gamma = 1.5, and vega = 0.8. Option 2: delta = 0.1, gamma = 0.5, and vega = 0.6 a. Compute the Initial portfolios delta, gamma, and vega. b. Compute the positions in Option 1, Option 2, and IBM (the underlying) to make the final portfolio delta, gamma, and vega neutral.