  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.
These costs are due to the inefficiency of the building, before an optimal
renovation date which depends on the carbon price process. Finally, we carry
out simulations based on the French economy and the house price index of
France. Our results allow to conclude that the order of magnitude of the
depreciation obtained by our model is the same as the empirical observations.
