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OPTIMAL TIMES TO BUY AND SELL A HOME

Matthew Lorig and Natchanon Suaysom ()
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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
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DOI: 10.1142/S0219024924500043

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