a) A financial institution has the following portfolio of over-the- counter options on sterling: Type Position Delta of Option Gamma of Option Vega of Option Call 1,500 0.55 1.5 1.8 Call -1,000 0.8 0.6 0.2 2.3 1.0 Put -500 Call -100 1.4 -0.4 0.7 1.8 There are two traded options available in the market, one with a delta of 0.85, a gamma of 1.25, and a vega of 0.6, and the second one with a delta of 0.5, a gamma of 0.9, and a vega of 0.7. i. Calculate the delta, gamma and vega of the portfolio. (5 marks) ii. What position in the traded option and in Sterling would make the portfolio delta-gamma-vega neutral? (10 marks) iii. If there were just one traded option available would you be able to make this portfolio delta-gamma-vega neutral? Explain. (5 marks)