"When dealing with a large-size position, dealer, upon exercise, synthetically become short an out-of-the-money option."
How does this work, I cannot see why this happens synthetically in particular?
Here's one scenario: dealer is long a deep in the money American put (say strike is K and the current stock price is S < K ), versus being short a european put with the same strike and final expiration. If the dealer exercises early the American put, he is now short the European put at K with a short stock hedge against it. Thus he is synthetically short a European call struck at K. ("synthetically" via put-call parity). I'm not sure if that's what is being referred to.
Here's the example of what is in the quote: dealer is long an ITM call. As a hedge the dealer is also short OTM put (with the same strike) and short stock. This is a "riskless" position, equivalent of a bond.
The underlying pays a dividend, and a day before the ex-date dealer exercises the call. The shares that dealer received from exercise are netted against his existing shorts to zeros, which leaves the dealer short an OTM put.