A trading desk holds the portfolio of over-the-counter options on the SP500 index shown in the table below. Delta of Gamma of Position Option Option Vega of Option Call -1,000 0.50 2.2 1.8 Call -500 0.80 0.6 0.2 Put -2,000 -0.40 1.3 0.7 Call -500 0.70 1.8 1.4 Figure 1: Option data for Problem 10. The desk would like to hedge the risks of this portfolio using an index option O with delta 0.6, gamma 1.5 and vega 0.8. a) What position in the traded option O and in index futures would make the portfolio both gamma neutral and delta neutral?