3. The following table describes a trader's options portfolio for a non-dividend paying asset: Contract Position Delta Gamma Vega Call -1000 0.3 0.7 0.7 Call -700 0.5 2.3 2 Put -1500 -0.6 1.4 1.6 Now answer the following questions: (a) Compute the delta, gamma and vega of the trader's options portfolio. (4 marks) (b) What would the trader's profit-and-loss (P&L) on the options portfolio be if the price of the underlying asset fell by $0.50? (2 marks) (c) What would the trader's profit-and-loss (P&L) on the options portfolio be if the volatility rose by 0.50%? (2 marks) (d) What should the trader do to make his portfolio delta-neutral? (2 marks) (e) Suppose another option is currently trading in the market with a delta of 0.8, a gamma of 0.75, and a vega of 0.8. What position in the underlying asset and this option will make his portfolio delta- and gamma-neutral? (3 marks) (f) Suppose the trader wants to use six-month futures in the underlying asset as hedging instruments. The risk-free rate is 4% per annum with continuous com- pounding. What position in the futures and the option described in part (e) will make his portfolio delta- and gamma-neutral? (3 marks) (g) What position in the underlying asset and the option described in part (e) will make his portfolio delta- and vega-neutral? (4 marks)