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Commercial Appraiser-Appraisal 310.337.1973 - Game Theory and Real Options: Analysis of Land Value and Strategic Decisions in Real Estate Development
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« Game Theory and Real Options: Analysis of Land Value and Strategic Decisions in Real Estate Development | Main | Investment under Uncertainty | Princeton University Press »

June 25, 2020


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Commercial Appraiser CRE BLOG, 310.337.1973

Real Options Pricing Model setup
When applied in real estate development, the real options can be considered an American
call option on the asset value of a building with the exercise price being the construction
or replacement cost. When the construction or replacement cost is subtracted from the
asset value of the building, the residual value is the maximum price that a developer
should pay for the piece of land to make it a zero NPV project. As stated above, this
classic NPV approach neglects the option value of waiting for future development. If the
real options pricing model is applied in the decision-making process, the option value
should be considered as well. In each period, developers should compare the residual
value with the option value to better understand their optimal action. The option premium
value (Cp) is defined as the difference between the residual value and the option value. If
the option premium value is positive, it means that the option value is higher than the
residual value, and the option to wait is more valuable than the decision to develop the
piece of land in this period, vice versa. A fundamental and pure form of the real options
pricing model will be used in this thesis to examine empirically the relationship between
the land value and the timing strategy of developers. Time t=0 is defined as the initial
period when the decision is about to be made. The property asset value (St) will either go
up by a multiple (u) to (St+0.25 = uSt) with the probability (p) or go down by a multiple (d)
to (St+0.25 = dSt) with the probability (1-p). The construction or replacement cost will
increase at an average growth rate throughout the periods. Since it is an American call
option, the option value (Ct) is defined as the maximum value between the residual value
and the option of waiting till next period. Key equations are as follows:

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