SO the coder at the end of the day for a trader what exactly will your product look like like?
In simple terms can you give an example and the reasoning why it would be different from normal PUT option?
That's easy to explain:
In a market with only CALL and FairPUT options the payout for FairPUT is the same as the payout for the CALL for the same z distance from K.
Ie. like in a fair game: you get the same reward regardless which side you bet, regarded you bet correct.
Ie. if CALL and FairPUT cost the same (depends on the params), then you can expect to get the same reward in both cases, in case you win.
Ie. in a 50:50 chance for both sides, the same reward is paid out for each side.
And: if CALL and PUT cost the same, then this is an indicator that both have the same probability for expiring ITM. But since both have the same probability and also do cost the same, then consequently both should also give the same payout. Q.E.D.
In contrast to that: with BSM PUT this is not the case! And that's its prime error!
Everybody can verify that fact with a BSM calculator (calculating twice: once for t, and then setting t near 0 to indicate expiration), or just doing simple arithmetics in the head.
Ie. in BSM the PUT is discriminated over the CALL; ie. PUT is not equally treated, as the PUT earns much less than the CALL, even if both have the same probability for expiring ITM and do cost the same...
(This analysis is comparing Long CALL and Long FairPUT with each other, not their Short versions, though the relation is the same with their Short versions as well)