Journal of Real Estate Finance and Economics, 25:1, 33±49, 2002
# 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.
Pricing Upward-Only Adjusting Leases
BRENT W. AMBROSE
University of Kentucky, Gatton College of Business and Economics, Lexington, KY 40506, USA
PATRIC H. HENDERSHOTT
University of Aberdeen, St Mary's, King's College, Aberdeen AB24 3UF Scotland, United Kingdom,
MAèGORZATA M. KèOSEK
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, 3200 N. Cramer St. Milwaukee,
WI 53201, USA
This paper presents a stochastic pricing model of a unique, path-dependent lease instrument common in the
United Kingdom and numerous commonwealth countries, the upward-only adjusting lease. In this lease, the
rental rate is ®xed at lease commencement but will be reset to the market rate at predetermined intervals (usually
every ®ve years) if it exceeds the contract rent. We derive a closed form expression for the market rent of a lease
with upward-only adjustments. Results indicate what the initial coupon rate on a 10-year lease with one reset
should be relative to that on a symmetric up-and-downward adjusting ``variable rate'' lease under various
economic conditions (level of real interest rates and expected drift and volatility of the underlying rental service
¯ow). We also consider the calculation of effective rents when free rent periods are given.
Key Words: leases, real options, effective rents
Grenadier (1995), using an endogenously derived term-structure for lease rates,
determines the equilibrium lease rates for many different types of leases under various
economic assumptions. In this paper, we utilize the concepts of market equilibrium
relationships among lease rates in development of a model for valuing securities with path-
dependent cash ¯ows. We apply this model to an interesting commercial lease contract
known as the upward-only adjustable lease.
The upward-only adjustable lease is a common commercial lease contract in the United
Kingdom and other former commonwealth countries, such as Australia and New Zealand
(Baum and Crosby, 1995). In this lease, the rental rate is ®xed for an extended term at lease
commencement, but the lessor has the option to have the rent periodically reset to the
market rate. If market rents have increased, then the lessor will increase the contract rent to
the market level. However, if market rents have declined, the rent remains unchanged.
The periodic open-market rent review was introduced into most leases in the United