a) Compute the delta, gamma and vega of the portfolio. What position is needed to make the portfolio delta neutral? [10 marks]
b) A new traded option (Option 1) is available on the market with a delta of -0.3, a gamma of 0.8 and a vega of 0.3. What are the positions needed to make the portfolio gamma and delta neutral? [10 marks]
c) Is it possible to make the portfolio gamma, vega and delta neutral using only Option 1? [5 marks]
d) Suppose that a second traded option is available (Option 2). The option has a delta of 0.2, a gamma of 0.2 and a vega of 0.6. Use Options 1 and 2 to make the portfolio gamma, vega and delta neutral.

Consider the portfolio shown in Table 1 comprised of four over-the-counter options on stock M: Option A (Call) Option B (Call) Option C (Put) Option D (Call) Position 370 -850 230 -470 Delta 0.3 0.2 -0.1 0.7 Table 1 Gamma 0.8 1.4 1.1 0.9 Vega 0.3 0.2 0.1 0.4