Question

What actions are required to both delta-hedge and gamma-hedge a written option
position?

Answer 1

To both delta-hedge and gamma-hedge a written option position one should create new hedges when the underlying asset’s delta changes. When an investor uses delta hedge alone then the position of the investor has protection from small changes in the underlying asset. Large changes will change the hedge and this can be remedied by adding a gamma hedge.

The number of underlying shares that will be bought or sold in a delta-gamma hedge will depend on the fact whether the underlying asset price is increasing or is decreasing.

In order to both delta hedge and gamma hedge a position in a certain option the market-maker will have to trade in another type of option. This will make the portfolio a self-financing portfolio.