a) A financial institution has the following portfolio of over-the-counter options written on Doogle shares:

Type	Position	Delta of Option	Gamma of Option	Vega of Option
Call	750	0.855	0.147	1.600
Call	-3,500	0.640	0.220	0.150
Put	-1,000	-0.420	0.179	1.150
Call	500	0.250	0.700	0.700

A traded option is available with a Delta of 0.8, a Gamma of 1.1, and a Vega of 0.45. i. What position in the traded option and in Doogle shares would make the portfolio both Gamma and Delta neutral? (5 marks) ii. Explain why a financial institution may want to keep their portfolio both Delta and Gamma neutral. (15 marks) iii. What position in the traded option and in Doogle shares would make the portfolio both Vega and Delta neutral? (5 marks) iv. If a second traded option with a Delta of 0.8, a Gamma of 1.35, and a Vega of 0.75 is available, what position in the traded option and in Doogle shares would make the portfolio Delta-Gamma-Vega neutral? (10 marks)

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