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

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?
Assume that all implied volatilities change by the same amount so that vegas can be aggregated.

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Position Delta of Gamma of Vega of option option option 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