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The option value of vacant land and the optimal timing of city extensions

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  • Teulings, Coen
  • Lange, Rutger-Jan

Abstract

Classic real options theory rests on two debatable assumptions: projects require a fixed investment and generate cash flows that follow a random walk. Relaxing both assumptions leads to radically different conclusions regarding the optimal timing of investment. We model investment using a Stone-Geary production function (Leontief and Cobb-Douglas are special cases) and growth as a mean-reverting Brownian motion. The solution method for this option valuation problem is non-trivial because the state space is two dimensional (level of the cash flow and its growth). For Leontief, the optimal policy is intuitive; the moment of investment involves a trade-off between the level of the cash ow and its growth. For Cobb-Douglas, in contrast, the optimal moment of investment depends only on the growth. More surprisingly, investment should be delayed when growth is high. This conclusion persists in the general Stone-Geary case. Applied to urban real estate, this suggests that up to 20% of cities should delay new construction because of high growth. The option value of vacant land may represent 60% of the value of new construction. High prices of vacant land may thus result from rational investor behavior rather than regulatory inefficiency. Our analysis should be widely applicable, for example to investment in high-growth companies.

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  • Teulings, Coen & Lange, Rutger-Jan, 2018. "The option value of vacant land and the optimal timing of city extensions," CEPR Discussion Papers 12847, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:12847
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    1. Esteban Rossi-Hansberg, 2004. "Optimal Urban Land Use and Zoning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(1), pages 69-106, January.
    2. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 597-624.
    3. Edward L. Glaeser & Joseph Gyourko, "undated". "The Impact of Zoning on Housing Affordability," Zell/Lurie Center Working Papers 395, Wharton School Samuel Zell and Robert Lurie Real Estate Center, University of Pennsylvania.
    4. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    5. Luis H. R. Alvarez, 2001. "Solving optimal stopping problems of linear diffusions by applying convolution approximations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 89-99, April.
    6. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    7. Edward L. Glaeser & Joseph Gyourko, 2005. "Urban Decline and Durable Housing," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 345-375, April.
    8. Glaeser, Edward L., 2008. "Cities, Agglomeration, and Spatial Equilibrium," OUP Catalogue, Oxford University Press, number 9780199290444.
    9. H. Dharma Kwon & Steven A. Lippman, 2011. "Acquisition of Project-Specific Assets with Bayesian Updating," Operations Research, INFORMS, vol. 59(5), pages 1119-1130, October.
    10. Arnott, Richard J & Lewis, Frank D, 1979. "The Transition of Land to Urban Use," Journal of Political Economy, University of Chicago Press, vol. 87(1), pages 161-169, February.
    11. Davis, Morris A. & Heathcote, Jonathan, 2007. "The price and quantity of residential land in the United States," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2595-2620, November.
    12. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    13. Capozza, Dennis & Li, Yuming, 1994. "The Intensity and Timing of Investment: The Case of Land," American Economic Review, American Economic Association, vol. 84(4), pages 889-904, September.
    14. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, May.
    15. Davis, Morris A. & Palumbo, Michael G., 2008. "The price of residential land in large US cities," Journal of Urban Economics, Elsevier, vol. 63(1), pages 352-384, January.
    16. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
    17. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
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    Cited by:

    1. Murray, Cameron, 2020. "A housing supply absorption rate equation," OSF Preprints 7n8rj, Center for Open Science.
    2. Cameron K. Murray, 2022. "A Housing Supply Absorption Rate Equation," The Journal of Real Estate Finance and Economics, Springer, vol. 64(2), pages 228-246, February.
    3. Ivo Gasic, 2024. "Disentangling Land Financialisation: Insights from Santiago de Chile's Land Lease‐Purchase Contracts," Tijdschrift voor Economische en Sociale Geografie, Royal Dutch Geographical Society KNAG, vol. 115(1), pages 28-41, February.
    4. Murray, Cameron K., 2020. "Time is money: How landbanking constrains housing supply," Journal of Housing Economics, Elsevier, vol. 49(C).

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    More about this item

    Keywords

    Real options; Mean-reverting growth; Real estate construction;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • R30 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location - - - General

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