I think that depends on what you mean with self-driving. My prediction is that in 2020 we will have slightly better driver assistance systems. Maybe a lane assist system which won't kill me if I don't babysit it on a road with construction ongoing and multiple lane markings or if corners get too tight. Maybe some limited self-driving, e.g. only available in dedicated areas like highway/autobahn.
Keep in mind that 2020 is 3 years, which is less than the development cycle of a car. Or in other words: If something should get released in 2020 you now would already see it driving around on the roads for first tests.
My personal prediction is that we will see reliable and advanced self-driving technology in mass production cars maybe in 2 full car generations from now - which is 2030.