Modeling the impact of Climate transition on real estate prices

In this work, we propose a model to quantify the impact of the climate transition on a property in housing market. We begin by noting that property is an asset in an economy. That economy is organized in sectors, driven by its productivity which is a multidimensional Ornstein-Uhlenbeck process, while the climate transition is declined thanks to the carbon price, a continuous deterministic process. We then extend the sales comparison approach and the income approach to valuate an energy inefficient real estate asset. We obtain its value as the difference between the price of an equivalent efficient building following an exponential Ornstein-Uhlenbeck as well as the actualized renovation costs and the actualized sum of the future additional energy costs (before and after the renovation date). These costs are due to the inefficiency of the building, before an optimal renovation date which depends on the carbon price process. Moreover, since the renovation increases the efficiency of the building, which is random, the future additional energy costs become smaller and even zero if the optimal energy efficiency is reached. Finally, we carry out simulations based on the French economy and the house price index of France. The findings support the conclusion that the order of magnitude of the depreciation obtained by our model is the same as the empirical observations.