Valuation of Reverse Mortgage

Abstract

This article provides an analytic valuation formula for reverse mortgage. We achieve this by utilizing the principle of balance between the expected gain and expected payment. The underlying model employs a jump-diffusion process to represent the dynamics of the house price, the Vasicek model to drive the instantaneous interest rate, and a bivariate distribution function to describe the longevity risk. We obtain, in particular, the formulas for the lump sum payment, joint annuity, increasing (decreasing) annuity, level annuity of reverse mortgage, and 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 analysis supports our theoretical results.