Commercial real estate valuation, development and occupancy under leasing uncertainty.

A model of commercial property valuation is developed where individual property owners are price takers and tenants randomly arrive and depart. Spot lease and tenant reservation prices are stochastic and correlated and can divert from but eventually revert back to market equilibrium. Within this framework we examine built property values and vacancy rates for varying parameter sets representing differing markets and economic conditions. We also examine how potential and existing vacancies, spot lease prices and tenant reservation prices feed back into development decisions. We demonstrate how preleasing acts as a hedge to the developer against the risk of leasing uncertainty.

Introduction

Researchers have long sought to develop models of the commercial real estate market that can rationally explain cyclical fluctuations in lease rates, development activity and structural occupancy levels. A related issue that has been largely ignored in the extant literature is the interaction between development activity and predevelopment occupancy levels. This interaction is directly observed in the real estate markets through the development of vacant units (speculative building) and the development of units that are already leased (preleasing). The reasons for what drives these phenomena, the levels of which seem to vary cyclically over time, have not yet been fully explored.

The vast majority of the theoretical research on occupancy (or conversely, vacancy) has focused on the owner-occupied residential market with relatively little examination of the commercial property markets. In addition, these models have not explained vacancy rates that are stochastic over time. Examples of the theoretical work on this topic include Wheaton (1990, 1999) and Williams (1995). Wheaton (1990) models the owner-occupied housing market where the number of households and units are fixed. The equilibrium house price and vacancy rate are determined in a static framework. In a similar model, but with a dynamic setting where an individual's implicit rents are stochastic, Williams (1995) determines house values and liquidity premiums, but again vacancy rates are constant. Wheaton (1999), in a stock-flow framework, examines how demand shocks can affect price and supply through development, but the market is assumed to always clear without vacancy.

A model of commercial development and stochastic occupancy is found in Grenadier (1995). In this real option based model, commercial property owners rent vacant space at a lease rate that is based on a downward sloping demand curve. Additionally, the model provides that tenants are always available, but because of the downward sloping demand, lessors may not choose to rent vacant units. Demand, through lease price levels, is stochastic, and there is a lease price that triggers a change in vacancy for an individual building. Lease prices also determine individual property development decisions where, after a time to build and only upon completion of the building, the owner will rent the optimal amount of space based on demand (price levels) at the time. His model computes the distribution of vacancy at the time of building completion. The results of Grenadier's model are primarily driven by the assumption of the downward-sloping demand curve faced by each individual property owner.

In this article we extend the Grenadier (1995) framework under the assumption that the commercial property market is competitive and individual property owners (lessors) are price takers. We model uncertain leasing demand as the frequency of tenant arrivals--the arrival of tenants able and willing to pay the market rental price--thus avoiding the assumption that tenants are always present to lease space at the current market lease price. At the time of a tenant arrival, lessors have the option to lease space and may avoid doing so if the lease price is not high enough to cover the additional costs incurred by adding a tenant. Additionally, we provide for the ability of individual property owners to lock in tenants before construction in order to hedge the risk of leasing demand changes and vacancies. In this way we can explain the development of additional vacant space (speculative building) concurrently with the development of already rented space (preleasing).

Our real option-based model explains structural (expected or steady state) single building vacancy rates in varying types of markets and development decisions when there is the ability to hedge leasing uncertainty risk through preleasing. Finally, we are also able to determine built property values within the context of the model and its assumptions.