A market maker has the following portfolio of options on the same underlying asset:

Type	Position	Delta of Option	Gamma of Option	Vega of Option
Call	-1,000	0.4	0.9	1.6
Put	600	-0.6	0.5	1.0
Put	-2,000	-0.5	1.4	0.55

(a) Calculate the delta, gamma and vega of the portfolio. What do the portfolio delta, portfolio gamma and portfolio vega you calculated mean? [9 marks]

(b) One traded option is available. It has a delta of 0.5, a gamma of 2.0, and a vega of 5.0. How can the portfolio be made both delta and gamma neutral? [4 marks]

(c) Two traded options are available. The first has a delta of 0.8, a gamma of 4.0, and a vega of 2.0. The second traded option has a delta of 0.5, a gamma of 2.0, and a vega of 5.0. How can the portfolio be made delta, gamma, and vega neutral? [10 marks]