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

Type	Position	Delta of Option	Gamma of Option	Vega of Option
Call	530	0.75	2.2	1.8
Call	-1,000	0.80	0.6	0.2
Put	-500	-0.40	1.3	0.7

A traded option is available with a Delta of 0.80, a Gamma of 1.1, and a Vega of 0.45. i. What position in the traded option and in Zamsung shares would make the portfolio Delta-Gamma neutral? ii. What position in the traded option and in Zamsung shares would make the portfolio Delta-Vega neutral? iii. Suppose there is a second traded option available with a Delta of 0.25, a Gamma of 0.9, and a Vega of 0.6. Calculate the position in the traded options and in Zamsung shares that would make this portfolio Delta-Gamma-Vega neutral.