THREE ESSAYS IN REAL OPTION MODELS OF REAL ESTATE DEVELOPMENT
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Abstract
Real estate developments make great applications for real option theory. However, current real option models for real estate development do not pick up the important features of real estate development such as the land-use right as an on-going lease agreement or the entitlement processes in every development project. We build and solve mathematically parsimoneous yet plausible stochastic-control models to capture these features and the models yield rich implications. We then test these implications empirically using manually-collected data.In chapter one, we model the real estate development process as a compound real option in a parsimonious continuous-time feedback control framework. The acquisition of a land-use right is the first option, and the decision to begin construction is the second option. We model the cost of maintaining the land-use right as a running cost during the waiting period before construction. This feature allows the running cost to be stochastic and interacts with both the decision to obtain the right and the decision to start construction. We obtain a closed-form solution for the value of the compound option and demonstrate rich implications using numerical examples. A higher running cost squeezes the two decisions together while a lower running cost encourages the acquisition of the land-use right and delays construction simultaneously.In chapter two, we recognize that entitlement process is highly risky and out of control of the investors in reality. Moreover, the real estate market in the U.S. has shown a trend towards more stringent entitlement regulation. Therefore, we model entitlement process as a separate stage in development process in which the investor has little control. In particular, we model the entitlement stage as a European style real option with a stochastic entitlement cost. We solve the model analytically. Our main result implies that, to the contrary of tradition real option theory, higher entitlement risk urges the investors to start entitlement process earlier in order to counter the lack of control.In chapter three, we test the empirical implications of entitlement in the previous chapter using hand-collected Charlotte local data of rezoning petitions. In particular, we collect waiting time, number of revisions, size of lot, decision outcome as well as other characteristics for rezoning petition from 2001 to 2012, published on Charlotte-Mecklenburg City Planning website. The results of negative binomial regressions confirm our earlier theoretical prediction that the investors start earlier when facing more difficult and riskier entitlement process. Moreover, house price is overall negatively correlated with the entitlement riskiness, which aggravates the hastening effect of entitlement risk.In conclusion, our real option models of land-use right and entitlement in real estate development prove to be mathematically novel, economically insightful, and show potential for wide applications.