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1. A financial institution has the following portfolio of options a stock:

Type	Position	Delta of Option	Gamma of Option	Vega of Option
Call	2,000	0.60	2.5	0.8
Call	200	0.80	0.6	0.2
Put	2,000	0.70	1.1	0.9
Call	500	0.70	1.8	1.4

An option is available with a delta of 0.5, a gamma of 2, and a vega of 1.5.

(a) What position in the traded option and in the stock would make the portfolio both gamma neutral and delta neutral?

(b) What position in the traded option and in the stock would make the portfolio both vega neutral and delta neutral?

(c) Another option with a delta of 0.2, a gamma of 0.5, and a vega of 1 is available. How could the portfolio become delta, gamma, and vega neutral?