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

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Question

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?

David · Accepted Answer

SOLUTION: 
The delta of the portfolio is  
 1 000 0 50 500 0 80 2 000 ( 0 40) 500 0 70 450                  
The gamma of the portfolio is  
 1 000 2 2 500 0 6 2 000 1 3 500 1 8 6 000                  
The vega of the portfolio is  
 1 000 1 8 500 0 2 2 000 0 7 500 1 4 4 000                
a.

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...

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