The last two decades have been characterized by a boom in the credit market for collateralized debt, namely mortgages and home equity loans, which led to a severe financial crisis. In this paper, we first document that players on both sides of the credit market, i.e. banks and households, were over-optimistic about future housing prices. We propose a parsimonious statistical approach to model biased expectations, aimed to capture information incompleteness about the data generating process. We then propose a more general model of a collateralized credit market, where households choose how much to borrow and whether to repay their debt, and banks decide the quantity of credit supplied, taking into account default possibilities. We show that optimistic expectations lead to severe distortions on the credit market, resulting in a large quantity of debt issued at a low price.