Monte Carlo Methods have been used in finance since the 1960's to simulate the various sources of said uncertainty that affect the value of instruments, portfolios or investments to calculate a value. This value is proportional to the likelihood of the events that affect it. Monte Carlo in finance is essentially a risk neutral evaluation. One of the main applications of Monte Carlo Methods in finance is Real Estate valuation. Estimating the value of real property is important to a variety of endeavors, including real estate financing, listing real estate for sale, investment analysis, property insurance and the taxation of real estate. The valuation models developed for financial assets are applicable for real assets as well. Since the market value of a property depends heavily on the values of surrounding properties and other factors in the neighborhood (like proximity to schools, safety of the neighborhood, etc.) it is possible to model them as a stochastic differential equation, and simulate using Monte Carlo methods.

Any attempt to predict the value of a property is curbed by the levels of uncertainty introduced by the different parameters in consideration. This makes Monte Carlo one of the better ways to estimate market values at some point in the future before deciding on an investment. This project introduces the notion of equity from the perspective of real estate and reviews the different methods used in real estate valuation, including the Discounted Cash Flow (DCF) model and the Adjusted Present Value (APV) model and the ways in which Monte Carlo methods are applied to these models. A Generalized Method of Moments estimator can also be put to use here. We also take a look at a Monte Carlo approach to Mortgage Pricing and the ways it is applied to Optimal Mortgage Refinancing and pricing when borrower default costs are unavailable or not observable.

This project is basically a review of the various Monte Carlo methods used for real estate valuation and mortgage pricing.

The project report is here


References

1. Glasserman, Paul. Monte Carlo methods in financial engineering. Vol. 53. Springer, 2003.

2. Hoesli, Martin; Jani, Elion and Bender, Andre Monte Carlo Simulations for Real Estate Valuation FAME Research Paper Series, International Center for Financial Asset Management and Engineering, rp148, 2005.

3. Giacotto, Carmelo and Clapp, John. Appraisal-Based Real Estate Returns under Alternative Market Regimes Journal of the American Real Estate and Urban Economics Association, V20,1, 1–24, 1992.

4. Baroni, Michel; Barthelemy, Fabrice and Mokrane, Mahdi Monte Carlo Simulations versus DCF in Real Estate Portfolio Valuation ESSEC Woking Papers, ESSEC Research Center, DR 06002, 2006.

5. Jost, Allen, et al. Real estate appraisal using predictive modeling. U.S. Patent No. 5,361,201. 1 Nov. 1994.

6. Rodda, David T., Ken Lam, and Andrew Youn. Stochastic Modeling of Federal Housing Administration Home Equity Conversion Mortgages with Low-Cost Refinancing. Real Estate Economics 32.4 (2004): 589-617.

7. Riddiough, Timothy J.; Thompson, Howard E. Commercial Mortgage Pricing with unobservable Borrower Default Costs. Journal of the American Real Estate and Urban Economics Association, V21,3, 265–291, 1993.

8. Zheng, Jin; Gan, Siwei; Feng Xiaoxia and Xe, Dejun. Optimal Mortgage Refinancing Based on Monte Carlo Simulation International Journal of Applied Mathematics, 42:2, 2012.