Pricing Upward-only Adjusting Leases

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 fixed at lease commencement but will be reset to the market rate at predetermined intervals (usually every five 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 flow). We also consider the calculation of effective rents when free rent periods are given.