The Option Value of Vacant Land: Don't Build when Demand for Housing Is Booming

Abstract

Urban structures and urban growth rates are highly persistent. This has far-reaching implications for the optimal size and timing of new construction. We prove that rational developers postpone construction not because prospects are gloomy, but because they are bright. The slow mean reversion in urban growth rates for the Netherlands and the United States (estimated at ∼0.07 per annum) implies that a substantial share of cities should optimally postpone construction due to high growth. Observed heterogeneity in floorspace density across cities can be explained not by differences in population levels, but in growth rates.

Solving penalised American options for jump diffusions using the POST algorithm

“…Interestingly, Theorem 1 requires neither bounded nor smooth problem data f, g. This contrasts with the majority of the vast literature on solutions to penalised HJB equations, which typically assumes bounded if not smooth problem data, c.f., in chronological order, [31, p. 9], [36, p. 180 While the POST algorithm (4) operates in function space, for computation we work in a bounded domain of some finite-dimensional (vector) space. This approach, also used in [22] and [23], involves fixing a natural number N to discretise the computational domain within the state space X , using grid points {x i : i = 1, . .…”