DP16023 The option value of vacant land: Don't build when demand for housing is booming
We consider an investor with the exclusive right to develop a property on a vacant piece of land, where the timing of the investment and the scale of the property are chosen optimally. The cash flow generated by the property follows a geometric Brownian motion with a stochastic drift, which is itself a mean-reverting Brownian motion. This setup allows for prolonged periods of above- or below-average growth. We prove that rational developers optimally postpone construction when prospects are gloomy, but also when they are bright: under sufficiently high growth, it is never optimal to invest. Perversely, the desire to ‘build big’ under high growth is stymied by a cost-of-capital argument, ultimately stifling investment. The combination of predicable growth and flexible investment may thus explain why construction in superstar cities appears sluggish,
