5. (20 points) Greek Letters A financial institution has the following portfolio of over-the-counter options on IBM stock: Type Position Delta of option Vega of option 1.8 Call Call Put Call - 1,000 -500 -2,000 0.2 Gamma of option 2.2 0.6 1.3 1.8 0.5 0.8 -0.4 0.7 0.7 1.4 -500 A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8. a. (5 points) What position in the traded option and options on IBM stock would make the portfolio gamma zero? b. (5 points) What is the gamma of the portfolio of options on IBM stock and 1000 shares of IBM? c. (5 points) What is the vega of the portfolio of options on IBM stock and 1000 shares of IBM? d. (5 points) What is the delta of the portfolio of options on IBM stock and 1000 shares of IBM