I think you are tilting at windmills.
Probably a good assessment.
Still, there are three obvious zones for the GBM stock (as noted previously, I follow the more distinguished and honorable convention of basing things off of the drift μ of the mean of the logarithm of the stock price as opposed to the expected rate of return on the stock α. α = μ + ½σ², for those following at home. And r = 0 in this example.): μ ≤ -½σ² ; -½σ² < μ < 0; and 0 ≤ μ. (Restoring r makes these μ ≤ r - ½σ² ; r - ½σ² < μ < r; and r ≤ μ.)
The first range is probably easy to reject: the risky asset has a lower expected rate of return than the riskless asset, AND over time
Pr{ST > BT} approaches 0? No.
The second range is something of a sweet spot, at least to my thinking: the risky asset has a higher expected rate of return than the riskless asset, but over time
Pr{ST > BT} approaches 0.
The third tests one's belief in risk aversion at least a little: the risky asset has a higher expected rate of return than the riskless asset, AND over time Pr{ST > BT} approaches 1.
With just fundamental assets, cheating into the third range a bit isn't too troubling: after a hundred years, there's very little possibility the stock will have underperformed the bond? And -- ?
But with derivative assets -- as someone noted earlier -- you can have payout probabilities approaching zero without significant time delay.
And in some respects, that's not too troubling: a derivative that pays out only in a six standard deviation event costs twice times its expected value? That's not going to break the bank; it might not even beat the bid-ask spread.
But extreme values are more a proof of concept matter: if you don't like the probability of loss or the expected loss of one derivative, no worries -- there's a derivative available where BOTH are lower!
For what WOULD affect prices, imagine the investor willing to sell something with a 48.65% chance of loss and only a 2.78% price over expected value ... which is what the house gets on a single zero roulette wheel bet on red or black. And then they need to net out the croupier's and the cocktail waitress' wages, the free drinks, the rent, etc.
Well, that's enough tilting at windmills for me for awhile.