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.