Real Estate Leases and Real Options

Abstract

This thesis builds on the real estate lease model of Grenadier which consists of the Black Scholes PDE and an upper reflecting boundary condition. Extending the method of images of Buchen, a new technique was developed to solve this class of problems. Problems that previously required difficult integration can now be solved with algebra and simple integrals. In addition, the compound option in this framework is solved using this new technique. To the best of our knowledge the solution of the compound problem has not been published. An interesting symmetry between this class of problems and the lookback option was also discovered and described in this thesis. The extension of the method of images to include problems with the reflecting boundary condition in the context of real estate leases was presented at the Financial Integrity Research Network Doctoral Tutorials at the University of Technology, Sydney, in 2006. The presentation was awarded the ``FIRN Best Paper Award''. This paper has been submitted to the Journal of Financial Mathematics for publication. The solution to the compound problem in the context of the upward-only market review option is the subject of the next paper.