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

(picture below)

A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.

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.

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