Optimal Pricing and Conditions for a Reverse Mortgage Lender in Canada

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Description of Research Project

A reverse mortgage is a financial instrument designed for Canadian families at or close to retirement who own a home. A reverse mortgage allows the owners to cash in part of the equity value of the home without having to sell the home at once. The homeowner makes no payments; the value owed continues to increase until the house is sold. The lender has several problems in setting the terms that are different from conventional mortgages and those terms are the main subject of this research.

A reverse mortgage has no set maturity date, though it is not a perpetual loan. In finance terms, it is a sort of option, but not one that is easily analyzed because of the lack of a maturity date and no set exercise price. The homeowner has a put option that can be exercised at any time, with the exercise price being the lesser of the value of the house and the value of the loan (with accrued interest). Since the value of the house will fluctuate over time in an unknown path, both the exercise price and the maturity date are unknown until the homeowners exercise the option to sell, or die, which forces the estate to exercise the option.

The key variable that the lender controls is the percentage of the value of the house that it will lend at a specific time. Another important factor is the forecast of future interest rates over a long time frame, since the reverse mortgage may be outstanding for decades.

The research will investigate these questions:

• How do reverse mortgage lenders set the terms of the contract?
• How should they set the terms to maximize their return and minimize their risk, while competing with other lenders?

The professor has extensive research and experience in stochastic processes and use of spreadsheets and can guide the student in whatever path seems appropriate to the student’s level of mathematical sophistication. This project will be valuable on the resume of any student who seeks employment in the financial services sector.

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Undergraduate Student Responsibilities

1. The student will determine the companies that offer reverse mortgages in Canada and how they operate. That includes learning and explaining all aspects of how the mortgages operate from both the lender point of view and the borrower point of view.

2. The student will find data on the transaction costs of valuing the house, setting up the loan contract and the expected cost of the eventual sale of the house.

3. The student will find data sources for the history of house prices in Canada and different areas of Canada.

4. The student will find data sources for movement of conventional and reverse mortgage interest rates in Canada during the last 10 years.

5. The student will access data on standard mortality rates in Canada.

6. The student will analyze the effect of the terms of the mortgages and how the firms set those terms. Depending on the level of technical and mathematical education the student has had, two different levels of sophistication are relevant:

a. A student who has experience with simulation software can develop a simulation of the effect of the increase in the loan value over time compared with the change in value of the house. It should be possible for student to learn how to use basic simulation software during the DARE project.

b. A student who is more comfortable with spreadsheets and scenarios will create multiple scenarios of different initial ages, mortality of the borrowers, and changes in house prices to focus on how much risk the lender may take with different percentages of house value loaned.

7. The student will write a brief summary paper about the findings of the research and prepare a poster for the celebration event in the fall.

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Qualifications Required

• Ideal, but not required: Completion of ADMS 3541 with at least 7.0 GPA
• Ideal, but not required: Completion of ADMS 4503 with at least 7.0 GPA or strong knowledge about Options; and/or experience with simulation.
• Basic understanding of mortgage products, interest rates, and financial risk. Familiarity with retirement finance, or option-like contracts is recommended.
• Ability to find and analyze Canadian housing price data, interest rate data, and mortality statistics, and interpret long-term trends.
• Experience with simulations or scenario analysis to model loan growth, house value changes, and lender risk.
• Working knowledge of Python (or similar) and/or Excel for data analysis, modeling, and visualization.