A financial institution currently has a portfolio with delta of 450 and gamma of 6,000. A traded option is available with a delta of 0.6 and a gamma of 1.5. How could the portfolio be made both delta neutral and gamma neutral? Sorry for this easy question, however I want to know how to make the portfolio delta and gamma neutral. Thanks a lot.
Your portfolio composition is not clear. To simplify, we assume that it consists of units of a stock and options on this stock. What you can do is to sell 4000 units of options that will bring it to gamma neutral, and then to balance the delta, you can buy 2,400-450=1,950 units of the stock.
I assume that stock is also available. Consider then
- What is the delta of stock? What is the gamma of stock?
- What position should the financial institution take in the traded option and the stock so that the gamma and delta of the portfolio are both 0?