Just to comment ont he title of this thread - the stock market is not what drives mortgage rates. Those are primarily driven by the 10y and 30y treasury bills. Of course, there is a negative correlation... when the stock market looks risky money pours into bonds, driving yields down. It also helps when the Fed sets borrowing rates at very low levels.
In practice, banks want to earn a slightly better return than what is offered on government bonds. Even though mortgages tend to be 30y notes, very few are carried to term, as people move or refinance on average every 7 years or so. Which is why the 10y treasury note matters so much.
Currently those sit at an historic 0.99% For comparison, for most of the previous 75 years they have sat somewhere between 3.00% and 6.00%. Even during the last 'low-interest' decade rates were typically above 2% During the 1970s and early 80s they routinely sat above 8% and briefly exceeded 12%.
As noted - we have no historic analog for bond rates being so low. So yes, I think if the banks decide that the next ~5-7 years we will see rates well below 2% we might see 30y mortgages below 3%.