A financial institution has the following portfolio of over-the-counter options on sterling:
Type Position Delta of Option Gamma of 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
A traded option is available with a delta of 0.7, a gamma of 1.5, and a vega of 0.8.
(a) What position in the traded option and in sterling would make the portfolio both gamma neutral and delta neutral?
(b) What position in the traded option and in sterling would make the portfolio both vega neutral and delta neutral?