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

This paper aims to model the housing price behavior in the Iranian market using three stochastic differential equations: the Black-Scholes model, Merton model, and geometric Brownian motion with nonlinear GARCH. The data of this study include monthly observations on housing prices between 2009 and 2018. Also, to estimate the coefficients of equations, we used the maximum likelihood approach, and the drift and diffusion parameters were 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 nonlinear 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, housing price is more affected by bad news and negative shocks. According to the estimated equations in the Iranian housing market and 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 volatility.