If I were to place a limit trade on a stock without compensation for placing a limit order, am I right in thinking that I would be giving a free option because the order make me commit and state my intention ahead of time? Are there formulas to quantify such option, and instruments to hedge it?
Unlike an option, you can pull your limit at any time so it's kinda not much of an option (except for real HFT guys).
Actually there has been recent academic work on exactly this subject. Modeling a limit order as having an embedded option to quantify the cost of adverse selection in market-making. As soon as I can remember who wrote the papers in question, I will post links.
The Price of Immediacy by Chacko, Jurek, and Stafford off Harvard Business School. http://www.people.hbs.edu/estafford/Papers/Immediacy.pdf The paper offers some theories on modeling limit orders as American options, along with some interesting empirical findings. Hope that helps!
IMO the price of a put option with the same expiration date and time as your limit order and with a strike price which is equal to your limit order price can give you a rough indication regarding the value of your limit order, as such put option is essentially a limit order to buy the stock and you are also being compensated for that (as opposed to a regular limit order on which you are not being compensated).