OPTIMAL TIMES TO BUY AND SELL A HOME

Matthew Lorig and Natchanon Suaysom ()
Additional contact information
Matthew Lorig: Department of Applied Mathematics, University of Washington, 4182 E Stevens Way NE, Seattle, Washington 98105, USA
Natchanon Suaysom: Department of Applied Mathematics, University of Washington, 4182 E Stevens Way NE, Seattle, Washington 98105, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2023, vol. 26, issue 08, 1-29

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 homebuyer, who can afford to pay only a fixed cash flow per unit time for housing. The cash flow is a fraction of the representative homebuyer’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 homebuyer finances the purchase of a home by taking out a mortgage. The mortgage rate paid by the homebuyer is fixed at the time of purchase and equal to the risk-free rate of interest plus a positive constant. As the homebuyer can only afford to pay a fixed cash flow per unit time, a higher mortgage rate limits the size of the loan the homebuyer 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.

Keywords: Home buying/selling; optimal stopping; nested optimal stopping; nonnegative concave majorant (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024924500043
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:26:y:2023:i:08:n:s0219024924500043

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024924500043

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().