Consider a trading book with the following options on a stock S: Type Position Delta of option Gamma of option Vega of option Put -100 -0.3 2.0 2.0 Call 100 0.4 0.5 0.5 Call -100 0.3 0.8 1.0 a. C. [2 points] Calculate the delta, gamma and vega of the trading book. b. [2 points) What position in the underlying is required to make the portfolio delta-neutral? [2 points] What position in the underlying is required to make the portfolio gamma-neutral? d. [4 points] Suppose that a traded option is available with a delta of 0.6, a gamma of 0.8, and a vega of 1.25. What position in the traded option and the underlying make the portfolio both vega-neutral and delta-neutral? e. [3 points) What is the gamma of the vega-neutral and delta-neutral portfolio