A financial institution has the following portfolio of over-the-counter options on sterling: A traded option is available

Question:

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

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

A traded option is available with a delta of 0.6, 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?

Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...