# Question: A financial institution has the following portfolio of over the counter options on

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 0.6, 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?

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.

(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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