2. Afinancialinstitutionhasthefollowingportfolioofover-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 0.6, a gamma of 1.5, and a vega of 0.8.

1. (a) What position in the traded option and in sterling would make the portfolio both gamma neutral and delta neutral?

   [10 marks]

2. (b) What position in the traded option and in sterling would make the portfolio both vega neutral and delta neutral?

   [10 marks]