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 -2,000 ,0.5, 2.2, 1.8; Call -1000, 0.8, 0.6 ,0.2 ;Put -4,000 ,-0.40, 1.3, 0.7 ;Call -1000 ,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. Is it possible to find a position in the traded option and in sterling that make the portfolio gamma neutral, vega neutral and delta neutral? Explain.