This question focuses on the risk management of European vanilla options, and re

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This question focuses on the risk management of European vanilla options, and refers to the data in the following table:

The portfolio consists of several traded European vanilla options. Option 1 and Option 2 are two other traded European vanilla options available to hedge the portfolio.

(i) What position in Option 1, Option 2 AND the Underlier would make the portfolio delta, gamma and vega neutral?

(ii) What are the limitations of this hedge?

Delta Gamma Vega Portfolio -450 -6000 -4000 Option (1) 0.6 1.5 0.8 Option (2) 0.1 0.5 0.6

Explanation / Answer

We solve

For Gamma,

6000+ 1.5w1 +0.5w2 =0

For vega,

4000+2.8w1 +0.6w2 =0

to get w1 = -3200 and w2 = 21600.

We require short position of 3200 in option 1 and long positions of 21600 in option 2. A long position of 240 in the asset is then required to make the portfolio delta neutral

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