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 -1,000 0.3 0.9 1.6 Call 600 0.2 0.5 1.0 Put -2,000 -0.6 1.4 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 0.8, a gamma of 4.0, and a vega of 2.0. How can the bank make the portfolio both delta and vega 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 6.0. How can the bank make the portfolio delta, gamma, and vega neutral? [10 marks] 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 -1,000 0.3 0.9 1.6 Call 600 0.2 0.5 1.0 Put -2,000 -0.6 1.4 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 0.8, a gamma of 4.0, and a vega of 2.0. How can the bank make the portfolio both delta and vega 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 6.0. How can the bank make the portfolio delta, gamma, and vega neutral? [10 marks]