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The Pricing of Embedded Options in Real Estate Lease Contracts

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    Abstract

    Leases and rental agreements often have options attached or embedded in them. These options sometimes depend on a number of economic variables such as the consumer price index (CPI), a real estate index and/or the value of real estate underlying the agreement. The evaluation of these options often involves the solution or approximation to a partial differential equation (PDE). This study analyzes the appropriate PDEs which model the situation where the lessee is granted an option to either purchase the property or to renew the lease at a price (rent) indexed to the CPI or some other readily measured economic variable. The PDEs that result from the usual contingent claim asset-pricing framework are derived and numerically solved using the finite difference method with absorbing boundaries. The value of an embedded option to renew a five year lease on class A office space in each of the ternty-five markets for which the National Real Estate Index reports quarterly rental data is estimated. An evaluation of the model’s "Greeks" confirm that the model conforms to financial intuition which provides support for the accuracy of the estimates.

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    File URL: http://aux.zicklin.baruch.cuny.edu/jrer/papers/pdf/past/vol15n03/v15p253.pdf
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    Bibliographic Info

    Article provided by American Real Estate Society in its journal Journal of Real Estate Research.

    Volume (Year): 15 (1998)
    Issue (Month): 3 ()
    Pages: 253-266

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    Handle: RePEc:jre:issued:v:15:n:3:1998:p:253-266

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    Postal: American Real Estate Society Clemson University School of Business & Behavioral Science Department of Finance 401 Sirrine Hall Clemson, SC 29634-1323
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    Web page: http://www.aresnet.org/

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    Postal: Diane Quarles American Real Estate Society Manager of Member Services Clemson University Box 341323 Clemson, SC 29634-1323
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    Web: http://aux.zicklin.baruch.cuny.edu/jrer/about/get.htm

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    1. Geske, Robert & Shastri, Kuldeep, 1985. "Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(01), pages 45-71, March.
    2. Joseph D. Albert & Willard McIntosh, 1989. "Identifying Risk-Adjusted Indifference Rents for Alternative Operating Leases," Journal of Real Estate Research, American Real Estate Society, vol. 4(3), pages 81-94.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    4. Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(01), pages 87-100, March.
    5. Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July.
    6. Courtadon, Georges, 1982. "A More Accurate Finite Difference Approximation for the Valuation of Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(05), pages 697-703, December.
    7. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-62, May.
    8. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
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    Cited by:
    1. Isil Erol & Kanak Patel, 2007. "Pricing the Default Option of Inflation-Indexed Mortgages Using Explicit Finite Difference Method," International Real Estate Review, Asian Real Estate Society, vol. 10(1), pages 48-92.
    2. Fang Fang & Lu Ruichang, 2009. "Is There a Term Structure? Empirical Evidence from Shanghai Office Rental Market," International Real Estate Review, Asian Real Estate Society, vol. 12(1), pages 23-38.
    3. Isil Erol & Kanak Patel, 2004. "Housing Policy and Mortgage Finance in Turkey During the Late 1990s Inflationary Period," International Real Estate Review, Asian Real Estate Society, vol. 7(1), pages 98-120.
    4. Liang, Zhaohui & Wang, Wei & Li, Shusheng, 2012. "Decomposition valuation of complex real options embedded in creative financial leases," Economic Modelling, Elsevier, vol. 29(6), pages 2627-2631.

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