Let say you have a stock that you can't short at your broker because its hard to borrow. Could you just buy a put and immediately exercise it making you short the stock?
yes you can, but i sure would take a hard look at the bid/ask spread the round trip of buying at the ask and selling at the bid can be very harsh on options of course you can make your own bid and ask, but then you are not guaranteed timely execution, especially if the option is moving fast. in most cases, it really is better to find a stock you can short
If I were to do this, I would just pick up some ITM puts right at expiration and get short with little cost. But I'd think there must be some limit because where is the broker going to find the stock for you to borrow if it was unborrowable in the first place?
That's right. If you can't get a borrow then you'll be bought in , probably $10 higher that you shorted. Best to buy an ITM put and play the short that way.