My questions are not about counterparty, they are about the monetary value of equity options.
(although your counterparty in US listed equity options will almost always be a market maker, who will most likely understand and use delta hedging when they post quotes on the exchange).
My questions are about delta hedging, which is a result of how to value (price) an option.
Which is the same as Black-Scholes:
Here’s a statement on counterparty: