Reverse Mortgages and Linked Securities: The Complete Guide to Risk, Pricing, and Regulation

APPENDIX B

Reverse Mortgage Analytics

Olivia S. Mitchell Insurance & Risk Management, The Wharton School, University of Pennsylvania

 

John Piggott School of Economics, University of New South Wales

 

 

 

 

At a general level, all reverse mortgage offerings that are self-financing must be priced so that the lending institution can expect to make back the money loaned plus interest over the term of the contract, after pooling risks across the set of loans sold. Here we provide an analysis of the lump-sum and annuity options for the reverse annuity product.

A simplified model of the loan amount can be specified by supposing a single borrower took out a loan in the form of a lump sum (LS) using his future home value as collateral. Then in a competitive market, the actuarially fair amount he could borrow would be set so the loan balance would equal in present value the anticipated value of the house at the time of sale. This may be defined as follows:

(B.1)

where r = expected future riskless rate of return, g = additional risk premium expected on housing investment above the riskless rate, m = additional risk premium expected on mortgage loans above the riskless rate, HEQ = home equity amount at the time the loan is taken out, _tp = proba bility of survival t periods from age x, maxAge = oldest possible survival age from life table (e.g., 110).

The lump sum (LS) simply grows at the mortgage ...