Sadly, no alternative currently exists. Well, none I know of.
There were some attempts like WebID and gpgAuth, but none is usable at the moment. They have to be dug out of dirt of oblivion, carefully analyzed and improved with important features they're missing to be usable for ordinary people (at least key escrow and sync - both completely optional, of course).
What I want from authentication system, is complete independence and full and ultimate control and ownership of my own identity. I don't want to trust, depend or even need any third party just to have account with someone. Not even if this third party is a domain name registrar, not even if I have a legal agreement with them.
When we had just usernames and passwords - it was exactly like that, except for mandatory emails thingy (but that's another story). I met someone, we introduce yourselves, negotiate a shared secret - and we're now acquaintances. With OpenID/OAuth/SAML/JWT/Persona this is no more the case - we have to call a notary and the notary will tell us who I am. And I really don't like this and want to see this fixed.
I want to revoke any possibility of any third party to revoke or otherwise deny my identity. They may assert my identity (say they know me and I'm a good lad) and revoke their assertion about my identity (i.e. say they don't trust me anymore), but not the fact who I am.