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 Long/Short Delta of each Gamma of each Vega of each position option option 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) 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 Long/Short Delta of each Gamma of each Vega of each position option option 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)