Abstract
In this paper, we suggest a Bayesian multivariate approach for pricing a reverse mortgage, allowing for house price risk, interest rate risk and longevity risk. We adopt the principle of maximum entropy in risk-neutralisation of these three risk components simultaneously. Our numerical results based on Australian data suggest that a reverse mortgage would be financially sustainable under the current financial environment and the model settings and assumptions.
Highlights
A reverse mortgage allows the owner of a home property to make a loan based on the value of the property while keeping the right to stay in the property for life
It is more flexible in terms of being able to incorporate more than one market price, allowing the use of different simulation methods, and pricing multiple risk factors within the same framework
Bayesian multivariate risk-neutral method has been ashown to be very flexible in dealing with multiple risks and setting marketpricing price constraints
Summary
A reverse mortgage allows the owner of a home property to make a loan based on the value of the property while keeping the right to stay in the property for life. Under the ageing population and the common problem of being asset-rich-cash-poor , reverse mortgages represent a financially feasible solution for millions of households This market has been growing quite steadily in Australia. We adopt the maximum entropy approach (Kogure and Kurachi 2010; Li 2010) in risk-neutralisation, which has some potential advantages over the other pricing methods such as the Esscher transform and Wang transform. It is more flexible in terms of being able to incorporate more than one market price, allowing the use of different simulation methods, and pricing multiple risk factors within the same framework.
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