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A financial institution has the following portfolio of over-the-counter options on a share position: ...

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Accounting

A financial institution has the following portfolio of over-the-counter options on a share position:

Type

Position (# of options)

Option Delta

Option Gamma

Option Vega

Call

500

0.5

2.2

1.8

Put

-500

-0.8

0.6

0.2

Call

-1,000

0.4

1.3

0.7

Put

-500

-0.3

1.8

1.4

A traded option is available with a delta of 0.6, a gamma of 1.2, and a vega of 0.8.

Calculate the overall delta, gamma, and vega position of the portfolio.

What position in the traded option and in share would make the portfolio both delta neutral and gamma neutral?

What position in the traded option and in share would make the portfolio both delta neutral and vega neutral?

Now assume a second traded option is available with a delta of -0.4, a gamma of 0.7, and a vega of 0.4. What position in the first traded option and in the second traded option would make the portfolio delta, gamma, and vega neutral?

Assume that all implied volatilities change by the same amount so that vegas can be aggregated. Also assume that options can be traded in units of one (not the usual contract of 100 options).

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