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A Lattice Framework with Smooth Convergence for Pricing Real Estate Derivatives with Stochastic Interest Rate

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Abstract

In this paper, a general binomial lattice framework, which is both computationally simple and numerically accurate, is developed for pricing real estate derivatives with stochastic interest rate. To obtain a computationally simple binomial tree with constant volatility, the transformation method and the probability density matching approach are introduced. A tilt parameter is then added to the jump movements to obtain smooth convergence. Therefore, the Richardson extrapolation (RE) can be used to enhance the convergence of the discrete binomial lattice models to continuous models when pricing European options. In addition, our smooth convergent models can also be applied to pricing American options.

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Notes

  1. The time-varying volatility is considered by Fabozzi et al. (2012) when the evolution of the volatility is deterministic. They pointed out that the volatility can be also considered as stochastic or following the dynamics of a GARCH process. However, this type of modelling will raise another layer of market incompleteness that will be difficult to resolve considering that real estate derivatives are not highly liquid yet as an asset class.

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Acknowledgments

The authors wish to express their sincere appreciation to the Editor in Chief, Professor Sirmans and the two anonymous referees for their helpful comments and suggestions, which helped to improve the quality of the paper tremendously. This work is supported by National Natural Science Foundation of China (No.71231005) and Research Fund for the Doctoral Program of Higher Education of China (20110142110068). Any remaining errors are solely ours.

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  1. School of Management, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Dong Zou & Pu Gong

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  1. Dong Zou
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  2. Pu Gong
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Correspondence to Pu Gong.

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Zou, D., Gong, P. A Lattice Framework with Smooth Convergence for Pricing Real Estate Derivatives with Stochastic Interest Rate. J Real Estate Finan Econ 55, 242–263 (2017). https://doi.org/10.1007/s11146-016-9576-x

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