Equilibrium Real Options Exercise Strategies with Multiple Players: The Case of Real Estate Markets
Wang, Ko, Zhou, Yuqing, Real Estate Economics
This article derives a closed-form solution for an equilibrium real options exercise model with stochastic revenues and costs for monopoly, duopoly, oligopoly and competitive markets. Our model also allows one option holder to have a greater production capacity than others. Under a monopolistic environment we find that the optimal option exercise strategy in real estate markets is dramatically opposite to that in a financial (warrant) market, indicating the importance of paying attention to the institutional details of the underlying market when analyzing option exercise strategies. Our model can be generalized to the pricing of convertible securities and capital investment decisions involving both stochastic revenues and costs under different types of market structures.
The option framework developed in the finance field has been used extensively for analyzing investment decisions related to nonfinancial assets. For example, Brennan and Schwartz (1985) and Paddock, Siegel and Smith (1988) use an option approach to evaluate natural resource investments and offshore petroleum leases. McDonald and Siegel (1986), Majd and Pindyck (1987) and Ingersoll and Ross (1992) explicitly analyze the impact of option value on capital investment decisions. McDonald and Siegel (1985) and Berger, Ofek and Swary (1996) address the termination option of an investment project. Childs, Ott and Triantis (1998) use the option valuation framework for analyzing the capital budgeting decisions of interrelated projects. Grenadier (1995) and Grenadier and Weiss (1997) apply the real options concept to value lease contracts and technological innovations. Schwartz and Zozaya-Gorostiza (2000) design a real options approach for evaluating information technology investments. However, it might be fair to say that, among all the areas embracing the application of the real options concept, real estate markets seem to draw the most attention from researchers. This is probably due to the large size of real estate markets and the availability of empirical data, which make it easier for researchers to empirically test or draw inferences from the real options theories developed in the field.
Titman (1985) and Williams (1991) are the first to apply the real options concept to value real estate developments. (1) Quigg (1993) and Holland, Ott and Riddiough (2000), among others, provide empirical evidence demonstrating that models based on the real options concept can indeed predict property values in real estate markets. Grenadier (1999) and Childs, Ott and Riddiough (2002) extend the literature by examining the impact asymmetric information and noise have on the exercise strategies of developers. On the other hand, recognizing that a development decision is not made in isolation and one developer's decision affects the decisions of others, researchers also advance the literature by analyzing option exercise strategies in an equilibrium setting. Williams (1993) first derives symmetric equilibrium exercise strategies for real estate developers. (2) However, because this equilibrium assumes that developers will exercise their options simultaneously, it might not be suitable to describe the exercise strategies of certain types of markets. For example, if there are three developers in an office property market and the minimum size of an office building is 20,000 square feet, under a symmetric equilibrium, all three developers will wait until the market demand reaches a level of around 60,000 square feet for each to build an office with a size of around 20,000 square feet. However, in reality, one developer will start construction when the demand level reaches about 20,000 square feet. Developers might build simultaneously (with a proportional share) if there is a large demand in a short time period that can be shared by them (say a demand for 200 single-family units in one month to be shared by 10 developers). Given this, it might be fair to say that the symmetric equilibrium characterized by Williams (1993) better describes the behavior of single-family property markets with a large number of developers (say 10 to 50), but may not be suitable for commercial property markets with fewer developers (say two to nine). …