1. Delta hedging is the first response, but if the market maker can complete a reversal then he/she will do so immediately. 2. If who buys the calls? The market maker!? What makes you say it doesn't show up in the volume figures? Volume is the number of contracts traded, each contract has a buyer and a seller.
The model that you use doesn't really make a whole lot of difference when you don't know what inputs to use, namely VOLATILITY. GARBAGE IN, GARBAGE OUT... if we know all other inputs into our model...dte, unerlying price, int rate, div, etc..and we also plug into our rmodel for instance for ABC aug 20 calls option price= .30 with stock price = 19.5..then a model will say this is a implied vol of y...basically it is impled because you can solve for it by all other observable variables...my model says implied = y...my neighbor who designed a different but useful model has an implied vol = y+.000001.... you and your model have implied vol = y+1.50...so then you look at your implied vol chart and say hey...this is too high and offer some calls at .30....I am y implied vol bid..so I buy you offer..and am bid out for 10,000 more..thanks for playing Einstein..how is this for a real world example?
My point exactly, if you can accurately forecast volatility then you can accurately price the options and buy the underpriced and sell the overpriced options.