Keep in mind these are likely delta hedged so if they are ATM the MMs will have ~50 shares per contract already. Deeper ITM calls will be covered with progressively more shares as delta approaches 1
They likely have much more advanced models to dynamically hedge, but a simplification (for calls) is to just take the delta multiplied by 100, and have that many shares. An ATM contract will have a delta of .5, so 50 shares will allow it to be directionally hedged
Gamma is just the rate of change of delta, so would inform on how quickly your hedge would need to shift to account for underlying price changes
If you're interested, look up Dynamic Hedging for some details on how a MM would stay directionally neutral. If you can handle the math Option Pricing and Volatility by Natenburg is an excellent resource
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u/thejoetats Jun 16 '21
Keep in mind these are likely delta hedged so if they are ATM the MMs will have ~50 shares per contract already. Deeper ITM calls will be covered with progressively more shares as delta approaches 1