Sunny Bank has the following portfolio of over-the-counter options on the same underlying asset: Type Position Delta of Option Gamma of Option Vega of Option Call -1,000 0.2 0.9 1.6 Put 600 -0.8 0.5 1.0 Put -2,000 -0.4 1.4 0.55 (a) Calculate the delta, gamma and vega of the portfolio [6 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 bank make the portfolio both delta and gamma neutral? [5 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 bank make the portfolio delta, gamma, and vega neutral? [8 marks] (d) What is meant by the vega of an option? How can you interpret a put option vega of 1.0? What are the risks in the situation where the vega of a position is large and negative? (4 marks] Sunny Bank has the following portfolio of over-the-counter options on the same underlying asset: Type Position Delta of Option Gamma of Option Vega of Option Call -1,000 0.2 0.9 1.6 Put 600 -0.8 0.5 1.0 Put -2,000 -0.4 1.4 0.55 (a) Calculate the delta, gamma and vega of the portfolio [6 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 bank make the portfolio both delta and gamma neutral? [5 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 bank make the portfolio delta, gamma, and vega neutral? [8 marks] (d) What is meant by the vega of an option? How can you interpret a put option vega of 1.0? What are the risks in the situation where the vega of a position is large and negative? (4 marks]