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 portfolio's delta, gamma, and vega.

b. Compute the positions in Option - 1, Option - 2, and IBM (the underlying) to make the final portfoliodelta, gamma, and vega neutral.