I was hoping someone could enlighten me as to how equity option market makers hedge in general, and whether they account for the effects of their purchases on the underlying share price when hedging in particular. I understand the general concept of remaining delta neutral, and that if a MM sells a call option, for example, they can purchase delta * 100 of the underlying stock in order to remain direction-neutral in the trade. However, in equities markets, is this the only strategy a market maker would generally engage in to remain delta-neutral? Or would they also attempt to purchase options, or engage in some other practice to try and keep themselves direction-neutral?
Also, do MMs have strategies to take into account how their own buying and selling of the underlying will affect the price and, in turn, their delta position? I'm curious with the recent meme stock explosions to what end a market maker would, for example, recognize that they've sold a large amount of options to the call side at varying strikes and if some of these options go in the money near expiration, how their own purchases will drive up the price and the underlying and cause more options to potentially end up in the money. Is this considered in any part of a hedging strategy?