IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2203.05545.html
   My bibliography  Save this paper

Optimal times to buy and sell a home

Author

Listed:
  • Matthew Lorig
  • Natchanon Suaysom

Abstract

We consider a financial market in which the risk-free rate of interest is modeled as a Markov diffusion. We suppose that home prices are set by a representative home-buyer, who can afford to pay only a fixed cash-flow per unit time for housing. The cash-flow is a fraction of the representative home-buyer's salary, which grows at a rate that is proportional to the risk-free rate of interest. As a result, in the long-run, higher interest rates lead to faster growth of home prices. The representative home-buyer finances the purchase of a home by taking out a mortgage. The mortgage rate paid by the home-buyer is fixed at the time of purchase and equal to the risk-free rate of interest plus a positive constant. As the home-buyer can only afford to pay a fixed cash-flow per unit time, a higher mortgage rate limits the size of the loan the home-buyer can take out. As a result, the short-term effect of higher interest rates is to lower the value of homes. In this setting, we consider an investor who wishes to buy and then sell a home in order to maximize his discounted expected profit. This leads to a nested optimal stopping problem. We use a nonnegative concave majorant approach to derive the investor's optimal buying and selling strategies. Additionally, we provide a detailed analytic and numerical study of the case in which the risk-free rate of interest is modeled by a Cox-Ingersoll-Ross (CIR) process. We also examine, in the case of CIR interest rates, the expected time that the investor waits before buying and then selling a home when following the optimal strategies.

Suggested Citation

  • Matthew Lorig & Natchanon Suaysom, 2022. "Optimal times to buy and sell a home," Papers 2203.05545, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:2203.05545
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2203.05545
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Leung, Charles Ka Yui & Tse, Chung-Yi, 2017. "Flipping in the housing market," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 232-263.
    2. James Albrecht & Pieter Gautier & Susan Vroman, 2016. "Directed Search in the Housing Market," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 19, pages 218-231, January.
    3. Carmona, Julio & Leon, Angel, 2007. "Investment option under CIR interest rates," Finance Research Letters, Elsevier, vol. 4(4), pages 242-253, December.
    4. Anglin, Paul M., 2004. "How long does it take to buy one house and sell another?," Journal of Housing Economics, Elsevier, vol. 13(2), pages 87-100, June.
    5. Tim Leung & Xin Li, 2015. "Optimal Mean Reversion Trading With Transaction Costs And Stop-Loss Exit," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    6. Savas Dayanik, 2008. "Optimal Stopping of Linear Diffusions with Random Discounting," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 645-661, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. de Angelis, Tiziano & Ferrari, Giorgio & Moriarty, John, 2016. "Nash equilibria of threshold type for two-player nonzero-sum games of stopping," Center for Mathematical Economics Working Papers 563, Center for Mathematical Economics, Bielefeld University.
    2. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    3. Essi Eerola & Niku Maattanen, 2018. "Borrowing constraints and housing market liquidity," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 27, pages 184-204, January.
    4. Xing Su & Zhu Qian, 2020. "State Intervention in Land Supply and Its Impact on Real Estate Investment in China: Evidence from Prefecture-Level Cities," Sustainability, MDPI, vol. 12(3), pages 1-15, January.
    5. Guo, Kevin & Leung, Tim, 2017. "Understanding the non-convergence of agricultural futures via stochastic storage costs and timing options," Journal of Commodity Markets, Elsevier, vol. 6(C), pages 32-49.
    6. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 32(3), pages 278-297, August.
    7. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    8. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, September.
    9. Combes, Pierre-Philippe & Decreuse, Bruno & Schmutz, Benoît & Trannoy, Alain, 2018. "Neighbor discrimination theory and evidence from the French rental market," Journal of Urban Economics, Elsevier, vol. 104(C), pages 104-123.
    10. Charles Ka Yui Leung & Joe Cho Yiu Ng, 2018. "Macro Aspects of Housing," GRU Working Paper Series GRU_2018_016, City University of Hong Kong, Department of Economics and Finance, Global Research Unit.
    11. Lester, Benjamin & Visschers, Ludo & Wolthoff, Ronald, 2015. "Meeting technologies and optimal trading mechanisms in competitive search markets," Journal of Economic Theory, Elsevier, vol. 155(C), pages 1-15.
    12. Cai, Xiaoming & Gautier, Pieter A. & Wolthoff, Ronald P., 2017. "Search frictions, competing mechanisms and optimal market segmentation," Journal of Economic Theory, Elsevier, vol. 169(C), pages 453-473.
    13. Manuel Guerra & Cláudia Nunes & Carlos Oliveira, 2021. "The optimal stopping problem revisited," Statistical Papers, Springer, vol. 62(1), pages 137-169, February.
    14. Yang, Chunpeng & Zhang, Zhanpei, 2021. "Realization utility with stop-loss strategy," The Quarterly Review of Economics and Finance, Elsevier, vol. 81(C), pages 261-275.
    15. Charles Ka Yui Leung & Joe Cho Yiu Ng & Edward Tang, 2020. "Why is the Hong Kong Housing Market Unaffordable? Some Stylized Facts and Estimations," Globalization Institute Working Papers 380, Federal Reserve Bank of Dallas.
    16. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.
    17. Yifan Chen & Jianhua Gang & Zongxin Qian & Jinfan Zhang, 2023. "Rationality test in the housing market: Project‐level evidence from China," Journal of Regional Science, Wiley Blackwell, vol. 63(3), pages 583-616, June.
    18. Lester, Benjamin & Visschers, Ludo & Wolthoff, Ronald, 2017. "Competing with asking prices," Theoretical Economics, Econometric Society, vol. 12(2), May.
    19. Egozcue, Martin & Fuentes García, Luis & Zitikis, Ricardas, 2012. "An optimal strategy for maximizing the expected real-estate selling price: accept or reject an offer?," MPRA Paper 40694, University Library of Munich, Germany.
    20. Gautier, Pieter & Siegmann, Arjen & van Vuuren, Aico, 2023. "Real-estate agent commission structure and sales performance," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 163-187.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2203.05545. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.