A financial institution has the following portfolio of over-the-counter options on sterling:

Delta of Gamma of Vega of Type Position Option Option 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 A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.

(a) What position in the traded option and in sterling wouldmake the portfolio both gamma neutral and delta neutral?

(b) What position in the traded option and in sterling wouldmake the portfolio both vega neutral and delta neutral?

AppendixLO1