First of all, usually these models are heavily adapted to a specific country (even for Europe), real estate class (housing, commercial) and market (secondary, primary). In general I would say it's very hard to directly apply standard quantitative tools (like MC) from finance for real estate market.
The models I've seen were not heavily quantitative. The most common approach is to build an equilibrium (supply/demand) model which also accounts for macroeconomic factors (interest rates, exchange rates, etc). For example, people try to estimate and forecast the purchasing power (credit availability) and capacity of new development projects. This may include many subtle things as modelling possible delays in development, taxes, policies, etc. Ideally liquidity and credit risks should be taken into account. This approach to modelling and forecasting is sometimes called top-down/bottom-up:
Top-down and bottom-up approaches to forecasting are commonly used in
the real estate industry. Macroeconomic (top-down) factors, such as
employment growth, gross domestic product (GDP), household formation,
and median household income drive both space-using demand and
long-term supply. Market construction pipeline data (bottom-up)
provides short-term supply information. Current vacancy (bottom-up) is
assessed, while future vacancy is derived from forecasted demand,
supply, and estimated total market inventory. Current rent (bottom-up)
is surveyed, while rent growth is forecast based on forecasted demand
and vacancy. Quantitative models built on long-term trends generate
baseline results, while adjustments are made to incorporate local
knowledge and short-term phenomena.
from Active Private Equity Real Estate Strategy
An important feature that one should account for while doing quantitative modelling in real estate is auto-correlation. Many researchers have documented the unusually strong predictable auto-correlation component. However, as I mentioned before, due to numerous unique features of the market this is hard to exploit on practice.
Also I'm aware about GIS-based and spatial models (e.g. spatial autocorrelation) for valuation of the real estate objects. But I've never seen them implemented in practice.
There are some articles on application of Monte Carlo methods in real estate valuation:
However, I cannot comment on how good they are.