| Presale of residential units refers to putting the units on sale before they are completed. The value of presale to the developer comes from the flexibility of timing the presale launch so as to optimize the expected payoff. We model the developer's optimal launch timing as a real option, and the purchaser's series of presale payments with the flexibility to default as compound options. By assuming a stochastic property price process, we derive model frameworks that a risk-averse developer should adopt in launching the presale under single and multiple payment schemes. The frameworks solve the optimal conditions, contract structures, and prices for the launch. We then extend the model to optimize developers' payoffs in monopolistic and imperfect market equilibria. Finally, by assuming a jump-diffusion demand shock process and based on game theoretic approach, we derive sub-game Nash equilibrium optimal strategies that determine when and at what price developers should launch for presale with stochastic or deterministic rare market events. All the models thus derived are subject to probabilities of purchaser defaults, which will happen if the contract prices are too high when compared to market prices. Our model frameworks confirm that the launch option values increase with increases in price growth rates and variances, but decrease in risk-free rates. Furthermore, developers tend to delay the launch when good events are anticipated, while launching presale earlier at lower prices in times of expected bad events. The equilibrium strategies also provide an alternative explanation to oversupply in property markets. We further illustrate effects of rare events on presale launching strategies through government intervention (particularly public housing and housing subsidies) and output flow uncertainty in competitive equilibrium. Our general optimal strategic models are robust in a few aspects. First, we include the time factor that is crucial for some real options. Second, only slight adjustments are required to cope with market changes, or jumps. Finally, the strategies thus derived can be extensively and flexibly applied to other real options which incur multi-stage contingent payoffs, and whose price processes are characterized by stochastic jump-diffusion process. |
