The Pricing of Embedded Options in Real Estate Lease Contracts

Abstract

Leases and rental agreements often have options attached or embedded in them. These options sometimes depend on a number of economic variables such as the Consumer Price Index (CPI), a real estate index and/or the value of real estate underlying the agreement. The evaluation of these options often involves the solution or approximation to a partial differential equation (PDE). This study analyzes the appropriate PDEs which model the situation where the lessee is granted an option to either purchase the property or to renew the lease at a price (rent) indexed to the CPI or some other readily measured economic variable. The PDEs that result from the usual contingent claim asset-pricing framework are derived and numerically solved using the finite difference method with absorbing boundaries. The value of an embedded option to renew a five year lease on class A office space in each of the twenty-five markets for which the National Real Estate Index reports quarterly rental data is estimated. An evaluation of the model’s “Greeks” confirm that the model conforms to financial intuition which provides support for the accuracy of the estimates.