3. A financial institution has the following portfolio of options a stock: Type Position Delta of Gamma of Vega of Option Option Option Call -2,000 0.60 2.5 0.8 Call -200 0.80 0.6 0.2 Put Call -2,000 -500 -0.70 1.1 0.9 0.70 1.8 1.4 An option is available with a delta of 0.5, a gamma of 2, and a vega of 1.5. (a) What position in the traded option and in the stock would make the portfolio both gamma neutral and delta neutral? (b) What position in the traded option and in the stock would make the portfolio both vega neutral and delta neutral? (c) Another option with a delta of 0.2, a gamma of 0.5, and a yega of 1 is available. How could the portfolio become delta, gamma, and; vega neutral?