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5 Housing Fin. Rev. 49 (1986)
On the Pricing of Shared-Appreciation Mortgages

handle is hein.journals/hsnfnrv5 and id is 51 raw text is: On the Pricing of Shared-Appreciation Mortgages by Frank H. Page and Anthony B. Sanders* This paper examines the impact of housing-value uncertainty as well as interest-rate uncertainty on the pricing of shared-apprecia- tion mortgages. Compared to a model in which housing values and interest rates are certain, the introduction of housing-value uncer- tainty lowers the share of appreciation required by the lender. Simi- larly, the introduction of interest-rate uncertainty lowers the share of appreciation required by the lender. If housing values and inter- est rates are positively correlated, a shared-appreciation position can be combined with a fixed-debt position in order to hedge against both housing-value uncertainty and interest-rate uncertainty. If housing values and interest rates are negatively correlated, the com- bination of a shared-appreciation position and a fixed-debt position will result in a highly speculative instrument. I. Introduction Recently, French and Haney [1984] examined the pricing of shared- appreciation mortgages under the assumption that housing-value changes are stochastic. This assumption allowed them to extend the seminal work of Dougherty, Van Order, and Villani [1982] who did not allow for uncertainty with regard to this variable. By incorporating un- certainty about housing values, French and Haney discovered that lenders would charge a lower share of appreciation relative to the share obtained by Dougherty, Van Order, and Villani under certainty. Department of Finance, University of Houston, University Park, 4800 Calhoun, Hous- ton, Texas 77004. Faculty of Finance, The Ohio State University, 318 Hagerty Hall, 1775 College Rd., Columbus, Ohio 43210-1309. * The authors would like to thank Steve Buser, Ken Dunn, Dan French, and Pat Hen- dershott for their helpful comments. Housing Finance Review 5, 49-57 (1986) © 1986 Elsevier Science Publishing Co., Inc. 0276-4415/86/$03.50

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