Financial Models and Real Estate

For some years, real estate and finance have become more and more interlinked. The application of the powerful tools developed in finance for this field of knowledge seems promising; mortgage valuation method developed by Kau, Keenan, Muller, Epperson (1992) being a major example of this. This article has applied arbitrage theory with two state variables (a rate and a house process) for pricing a mortgage considered as a contingent claim made of a loan, a prepayment option and a default option. Some well-known arguments lead to a valuation's PDE (partial differential equation) solved numerically. The concepts used in finance are built on market reality and assumptions made in stochastic calculus relying on the possibility of actual operations; for example the hedging or the concrete exploitations of arbitrage opportunities when they appear. These hypotheses are not purely formal or only useful for solving a mathematical problem; they are leaning on the distinctive characteristics of the studied object. The purpose of this article is to re-examine the use of financial models in the light of specific features of real estate in order to see if the requirements of theory are entirely satisfied with this particular asset. This paper is organized as follows. After a literature review of the optional models for mortgages, the demonstration leading to the fundamental valuation's PDE is recalled, trying to be as explicit as possible whenever a market assumption is necessary. Then the theoretic requirements are discussed, confronting them to the actual situation of the real estates. Does the riskless portfolio exist when dealing with buildings? Does arbitrage activity exist and which assets could be chosen for realising an arbitrage portfolio? Numerous difficulties appear making a blind application of this PDE model rather doubtful. In order to better understand the size of a potential mispricing, one of the difficulties relating to the valuation of contingent claims depending on a real estate is studied. To this end a simplified reverse mortgage is presented and the impact of the appraisal accuracy (concerning the house associated to this contract) is studied for the put option embedded in the mortgage. Usually, estimation can be considered correct if it stays within -10% and 10% of the real price. This accuracy is very reasonable when valuing such a complicated asset as a house; but unfortunately this good appraisal quality is going to produce a bad financial quality for the put's pricing. Results show that errors can be very important, up to 100 %; the leverage effect of an option acting as a noise amplifier.