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 -2,000 ,0.5, 2.2, 1.8; Call -1000, 0.8, 0.6 ,0.2 ;Put -4,000 ,-0.40, 1.3, 0.7 ;Call -1000 ,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. Is it possible to find a position in the traded option and in sterling that make the portfolio gamma neutral, vega neutral and delta neutral? Explain.

Answer 1

First, we will calculate Portfolio Gamma, Delta, and Vega

• Portfolio Delta = Sum of ( Position * Delta) in each Position = -900
• Portfolio Gamma =  Sum of ( Position * Gamma ) in each Position = -12,000
• Portfolio Vega =  Sum of ( Position * Vega ) in each Position = -8000

Now The Traded Option Have   a delta of 0.6, a gamma of 1.5, and a vega of 0.8.

To Make the Portfolio Gamma Neutral no of Options Require = Portfolio Gamma /  Option  gamma = -12,000 /  1.5 = 8000

Vega Value become = No of Options * vega + Portfolio Vega = 8000*0.8 - 8000 = 6400 - 8000 = -1600

Since Both are not getting zero at a time it is not possible to Make portfolio gamma neutral, vega neutral and delta neutral at a time with a single option given here.