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. iv. If the financial institution sets the total Delta and Gamma of their portfolio of options on Zamsung to zero, the portfolio will be protected against fluctuations in the spot price of Zamsung stocks. In this case, the financial institution can forget about its exposure to Zamsung. Discuss.