When I buy or sell a stock, the transaction will increase the stock's trading volume. Instead, suppose I buy an option and decide to exercise it immediately (for whatever reason). When I exercise a call option, I am buying stock from the counterparty. When I exercise a put option, I am selling stock to the counterparty. Does options exercise increase a stock's trading volume?
If satisfying the assignment/exercise of the contract results in transfer of shares to the counterparty, there is no stock exchange transaction since the trade occurs at the strike price between the two counterparties.
If one of the parties needs to acquire the shares in order to deliver or if one of the parties chooses to close the assigned shares then a transaction will occur on the stock exchange.