A dynamic model of house price

In this paper, we build the rationale of the financial intermediate's decision of making loans to potential home buyers over an infinite time horizon. In the first period "good" borrowers with stable future income flows receive loans and buy homes. In later periods, the intermediate securitizes the loans to raise new capital and makes loans to some of the "bad" borrowers with uncertain future income flows. Currently, we simplify the securitization as a tool to raise capital without cost over time. This unrealistic simplification should be improved in later work. The financial intermediate calculates the expected payoffs in different scenarios under the realizations of uncertainty to decide whether to make loans to a new borrower and whether to liquidate a house if the owner is short of liquidity in the short run. After clarifying the sequence of moves of different agents within each period, we compute the financial intermediate's decision rule described by a Bellman equation. Then we simulate borrowers' income realization and produce a figure of house price as well as value function over time.