Question

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

Market makers buy and sell just like anyone else with different products. Obviously buying low selling high is the goal. This process is selected and done by demand and supply of the instrument or product not by personal interest. One way that market makers in the derivatives market that they can control this risk is by Delta Hedging. The market maker calculates the purchase of the option delta and takes an offsetting position. This delta-hedged strategy is commonly used in the markets especially these days. That investor usually invests own capital to do this. The Black-Scholes model is a key part of this.

Answer 1

First, we should proceed with the gamma heading. To Gama hedge a portfolio, we have to take some extra position in the existing options to gamma hedge the portfolio. An example of a gamma hedge is when you buy a put, which gives you negative delta and positive gamma, then sell a call to zero out your gamma but give you even more negative delta.

After that we have to think of delta hedging the overall portfolio (old portfolio + some new options). If overall delta is negative now, we have to ho long in the shares of the underlying by the same amount (as stock has delta of). Else, overall portfolio has positive delta, in which case we have to go short in the underlying stock by the same amount.

In this way, out portfolio will be gamma and delta hedged simultaneously.

Please do rate me and mention doubts in the comments section.