A financial institution has a portfolio of over-the-counter options on the same underlying asset. Following details are available about this portfolio:

Type	Position	Delta of Option	Gamma of Option	Vega of Option
Call	-2,000	0.3	0.5	1.6
Call	700	0.4	0.8	1.2
Put	-1,800	-0.5	1.5	0.5

(a) Calculate the delta, gamma and vega of the portfolio. Provide an interpretation of the numbers (portfolio delta, portfolio gamma and portfolio vega) you calculated. [9 marks]

(b) One traded option is available. It has a delta of 0.5, a gamma of 2.5, and a vega of 3.0. How can the bank make the portfolio both delta and gamma neutral? [4 marks]

(c) Does a delta and gamma neutral portfolio need re-balancing? Why/why not? [2 marks]