Question: A financial institution has the following portfolio of over-the-counter options on a certain stock:
Type Position Delta Gamma Vega
call -4,000 0.6 2.3 1.4
put -7,000 -0.3 1.1 0.6
call -2,500 0.9 0.2 2.5
Two traded options are available, one with a delta of 0.2, a gamma of 0.5, and a vega of 2.3, and the other with a delta of 0.7, a gamma of 1.5, and vega of 0.8. What position would the financial insistution need to take in these options and the underlying stock to make the portfolio delta, gamma, and vega nuetrual?