Question 8: A financial institution has the portfolio consisting of short position in 100,000 call options with exercise price of 150, and life of 3 months. The underlying is non-dividend paying stock characterised by annual volatility of 28%. The delta of the option is 0.60, the gamma is 0.010 and the vega is 30. In the table below the Greek letters for each of the available options are compared Option Type of option Strike Delta Gamma Vega number: price 1 Call 160 0.42 0.0200 28.0 2 Call 170 0.18 0.0150 30.0 a. b. What position in the traded option 1 and in underlying stock would make the portfolio both gamma neutral and delta neutral? (3 marks) What position in the traded options and in underlying stock would make the portfolio delta, gamma, and vega neutral? (3 marks) Please give the example of two options (defined in terms of Greek letters) on underlying stock, which cannot be used to make the above portfolio delta, gamma and vega neutral. Please explain your choice. (2 marks) C. Question 8: A financial institution has the portfolio consisting of short position in 100,000 call options with exercise price of 150, and life of 3 months. The underlying is non-dividend paying stock characterised by annual volatility of 28%. The delta of the option is 0.60, the gamma is 0.010 and the vega is 30. In the table below the Greek letters for each of the available options are compared Option Type of option Strike Delta Gamma Vega number: price 1 Call 160 0.42 0.0200 28.0 2 Call 170 0.18 0.0150 30.0 a. b. What position in the traded option 1 and in underlying stock would make the portfolio both gamma neutral and delta neutral? (3 marks) What position in the traded options and in underlying stock would make the portfolio delta, gamma, and vega neutral? (3 marks) Please give the example of two options (defined in terms of Greek letters) on underlying stock, which cannot be used to make the above portfolio delta, gamma and vega neutral. Please explain your choice. (2 marks) C