Existing volatility models normally emphasize the behavior of prices in a temporal sense and comparatively few studies have explicitly analyzed the spatial variation of volatility. This paper proposes a flexible spatial volatility model for squared returns using a Box-Cox transformation that includes the linear and log-linear forms as special cases, thus providing a unified framework for simultaneously testing space-varying volatility and its functional form. The maximum likelihood method is used to estimate the model and Monte Carlo simulations are conducted to investigate the finite sample performance of the maximum likelihood estimator. The use of the model is also illustrated by a substantive application to housing price data in the city of Chicago. The estimation results suggest that housing returns in Chicago show the volatility exhibits strong spatial dependence and the log-linear functional form is appropriate. In the final log-linear model, a new practical indicator, called neighborhood elasticity, is proposed that determines how volatility in one neighborhood is linked to that in surrounding neighborhoods. From a practical point of view, this indicator provides a tool to help policy-makers avoid volatility transmission and the risk of contagion in the housing market.