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

on sterling:

Type	Position	Delta of Option	Gamma of Option	Vega of 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

A traded option is available with a delta of 0.7, 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?

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