SECTION B There are TWO questions in Section B. Candidates must answer both questions. Always show your work fully. Present your results with 4 decimal places. QUESTION THREE A financial institution has the following portfolio of over-the-counter options written on Minstagram shares: Type Position Delta of Option Gamma of Option Vega of Option Call -3,000 0.65 1.5 1.30 Call -2,000 0.70 0.6 0.85 Put -750 -0.35 1.8 0.70 -50 Call 0.70 1.7 1.40 A traded option is available with a Delta of 0.8, a Gamma of 1.1, and a Vega of 0.45. a) What position in the traded option and in Minstagram shares would make the portfolio both Gamma and Delta neutral? (5 marks) b) Suppose the financial institution is trying to minimise their exposure to changes in the underlying asset price. Explain why the financial institution may want to keep their portfolio both Delta and Gamma neutral. (10 marks) c) Suppose there is a second traded option with a Delta of 0.65, a Gamma of 0.4, and a Vega of 0.8. What position in the traded option and in Minstagram shares would make the portfolio Delta-Gamma-Vega neutral? (10 marks) [TOTAL: 25 MARKS SECTION B There are TWO questions in Section B. Candidates must answer both questions. Always show your work fully. Present your results with 4 decimal places. QUESTION THREE A financial institution has the following portfolio of over-the-counter options written on Minstagram shares: Type Position Delta of Option Gamma of Option Vega of Option Call -3,000 0.65 1.5 1.30 Call -2,000 0.70 0.6 0.85 Put -750 -0.35 1.8 0.70 -50 Call 0.70 1.7 1.40 A traded option is available with a Delta of 0.8, a Gamma of 1.1, and a Vega of 0.45. a) What position in the traded option and in Minstagram shares would make the portfolio both Gamma and Delta neutral? (5 marks) b) Suppose the financial institution is trying to minimise their exposure to changes in the underlying asset price. Explain why the financial institution may want to keep their portfolio both Delta and Gamma neutral. (10 marks) c) Suppose there is a second traded option with a Delta of 0.65, a Gamma of 0.4, and a Vega of 0.8. What position in the traded option and in Minstagram shares would make the portfolio Delta-Gamma-Vega neutral? (10 marks) [TOTAL: 25 MARKS