A Stochastic Approach to Model Housing Markets: The US Housing Market Case
American Institute of Mathematical Sciences (2018) Doi 10.3934/naco.2018030
Posted: 6 Apr 2020
Date Written: December 8, 2018
This study aims to estimate the price changes in housing markets using a stochastic process, which is defined in the form of stochastic differential equations (SDEs). It proposes a general SDEs system on the price structure in terms of house price index and mortgage rate to establish an effective process. As an empirical analysis, it applies a calibration procedure to an SDE on monthly S&P/Case-Shiller US National Home Price Index (HPI) and 30-year fixed mortgage rate to estimate parameters of differentiable functions defined in SDEs. The prediction power of the proposed stochastic model is justified through a Monte Carlo algorithm for one-year ahead monthly forecasts of the HPI returns. The results of the study show that the stochastic processes are flexible in terms of the choice of structure, compact with respect to the number of exogenous variables involved, and it is a literal method. Furthermore, this approach has a relatively high estimation power in forecasting the national house prices.
Keywords: Housing index, Mortgage rate, Stochastic differential equations, Forecasting, Calibration
JEL Classification: 62P05, 91G60, 91G80, 81T80
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