Urban development under discrete random shocks

This paper investigates the effects of discrete random shocks to the urban development decision and the price of land. The urban development has three important characteristics: investment irreversibility, uncertainty of future payoffs and an option to postpone the investment. In contrast to the existing literature that treats uncertainty as continuous time stochastic process, this paper considers uncertainty as a discrete time stochastic process (discrete random shocks) with two different sources of uncertainty. One is the uncertainty of the time when shock occurs, and the other is the uncertainty of the jump size shock incurs. This paper contributes to the real option literature in the following ways. First, the approach developed here can be applied to other lump sum cost investment decision under discrete random shocks; second, this paper is the first to study how discrete random shocks affect the urban development and the price of urban and agricultural land. We show that (i). The price of urban land is uniquely determined by the current rent, the mean arrival rate of random shocks and the expected value of jump size; (ii). If jump sizes with shock occurrence are all positive, landowners will convert their agricultural land to urban use when the urban rent first hits agricultural rent plus capital opportunity cost; (iii). If jump size with shock occurrence is up and down with positive probability, then (a). The higher probability of random shocks may (a.1) deter urban development and decrease the price of agricultural land; (a.2) deter urban development and increase the price of agricultural land; (a.3) encourage urban development and increase the price of agricultural land; (b). The more spread of random jumps may (b.1) deter urban development and decrease the price of agricultural land; (b.2) deter urban development and increase the price of agricultural land; (b.3) encourage urban development and increase the price of agricultural land.Business, Sauder School ofGraduat