Show work. A financial institution has the following portfolio of OTC options on euros:
Type Position Delta Gamma Vega
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 with a delta of 0.6, a gamma of 1.5, and a vega of 0.8 is available.
a) What position in the traded option and in euros would make the portfolio both delta and gamma neutral?
b) What position in the traded option and in euros would make the portfolio both delta and vega neutral?