Pricing Upward-Only Adjusting Leases

Abstract

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. Numerical results indicate how the initial coupon rate should be set 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 during either a market collapse or a steady-state drift.