Consider the portfolio shown in Table 1 comprised of four over-the-oounter options on the Shell stock, that was trading at 19.48 at the close of the trading day 18th March 2022: Table 1 -m mm Option b (Call) \"HE-m _----EEI Option d (Call) ----m a) Compute the delta, gamma and vega of the portfolio. What position is needed to make the portfolio delta neutral? [6 marks] b) A new traded option (Option X1) is available on the market with a delta of -0.2, a gamma of -0.1, a vega of 0.3 and a theta of -0.1. Is it possible to make the portfolio gamma and delta neutral? If yes, what are the positions needed to make the portfolio gamma and delta neutral? If not, explain in detail why it is not possible. [6 marks] o) Is it possible to make the portfolio vega and delta neutral by using Option X1? If yes, what are the positions needed to make the portfolio vega and delta neutral? If not, explain in detail why it is not possible. [6 marks] d) Suppose that a second traded option is available (Option X2). The option has a delta of 0.5, a gamma of 0.2, a vega of 0.4 and a theta of -0.4. Is it possible to make the portfolio vega, gamma and delta neutral by using options X1 and X2? If yes, what are the positions needed to make the portfolio vega, gamma and delta neutral? If not, explain in detail why it is not possible. [7 marks]