Consider a portfolio has a Delta of 90, a Gamma of -17, and a Vega of -10.

(a) A traded option is available with a Delta of 0.2, a Gamma of 0.01, and a Vega of 0.02. What position in the traded option and/or underlying stock would make the portfolio both Delta neutral and Vega neutral? Show your work step by step. (2 marks)

(b) There are two traded options available:

	Delta of option	Gamma of option	Vega of option
Traded options 1	0.2	0.01	0.02
Traded options 2	-0.1	0.05	0.02

What position in the traded option and/or underlying stock would make the portfolio Delta, Gamma, and Vega neutral? Show your work step by step. (5 marks)

(c) Assume Bank Monash has the following positions on a stock in its portfolio.

Option position	Long/Short	Delta of each option	Gamma of each option	Vega of each option
100 Call	Long	0.10	0.02	0.01
200 Call	Short	0.01	0.05	0.02
100 Put	Short	-0.50	0.05	0.03
100 Put	Short	-0.10	0.04	0.04

What is the aggregate Delta of the portfolio? Show your work step by step. (1 mark)