Publication TypeJournal Article
Year of Publication2018
JournalDynamic Systems and Applications
Start Page895
Date Published12/2018
AMS Subject Classificationjoint annuity, jump-diffusion, lifetime model, reverse mortgage, valuation, Vasicek model

Utilizing the principle of balance between expected gain and expected payment, this work obtains the analytic valuation formula for reverse mortgage. In particular, we provide the formulas for the lump sum payment, joint annuity, increasing (decreasing) annuity, and level annuity of reverse mortgage. We also derive the valuation equation that the variable payment annuities satisfy. We then discuss the monotonicity of the lump sum, annuity, and annuity payment factors with respect to the parameters associated with the home price and the interest rate model. Finally, we analyze the sensitivity of the joint annuity with respect to the parameters associated with the home price, interest rate, and lifetime model. The numerical results show that the average return of home price exerts a dominating influence on the joint annuity, followed by the mean reversion level of interest rate, and both of them have stronger impact on the annuities of younger applicants than those of older applicants. Meanwhile, the initial age of male and that of female produce asymmetrical effect on the joint annuity. Remarkably, the dependence of joint-lifetime significantly affect the joint annuity value. In case that the male and female initial ages are both less than 80 years old, annuity values on average increase  approximately 4.5%, and the greatest increment of annuity value approaches 9%.

Refereed DesignationRefereed
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