Price Jump Diffusion in Iranian Housing Market (Merton Model and NGARCH Approach)

Abstract

The purpose of this paper is to model the behavior of the housing price in the Iranian market using stochastic differential equations. The data of this study include monthly observations on housing prices for the period from 2009 to 2018. To model the behavior of the housing market, three stochastic differential equations have been used: Black-Scholes model, Merton model, and geometric Brownian motion with nonlinear GARCH. Also, in order to estimate the coefficients of equations, we used the maximum likelihood approach, and the drift and diffusion parameters are calculated. The findings suggest that the efficient-market hypothesis does not hold in the Iranian housing market since the sudden jump under systematic risks is indicative of an increase in inefficiencies in the housing market. In this paper, we also use the non-linear GARCH (NGARCH) model based on the Merton model to investigate the impact of good and bad news and positive and negative shocks. According to the results of the NGARCH model, the housing price is more affected by bad news and negative shocks. In total, according to the estimated equations in the Iranian housing market and given the maximum likelihood function, the geometric Brownian model with stochastic NGARCH-based fluctuations has more explanatory power than the Merton model and the geometric Brownian model with constant fluctuations.