The institutions for financing owner-occupied housing have not progressed as they should, and the financial innovation that has followed the financial crisis of 2007-9 has not been focused on improving the risk management of individual homeowners. This paper lists a number of barriers to housing finance innovation, and in light of these barriers, the problems of some major innovations of the past and future: self-amortizing mortgages, price-level adjusted mortgages (PLAMs), shared appreciation mortgages (SAMs), housing partnerships, and continuous workout mortgages (CWMs). Modern financial theory suggests some fundamental modifications to the institutions supporting housing, and yet nothing fundamental has happened to the standard mortgage contract between the homeowner and originator since the long-term fixed-rate self-amortizing mortgage was widely adopted in the U.S. in the 1930s, replacing the then-standard 3-5-year balloon payment mortgage (Bartlett 1989, Green and Wachter, 2005). The U.S. mortgage industry has maintained this type of mortgage despite the mathematical finance revolution of the second half of the twentieth century, which suggests many important innovations.