FAIR PRICING OF REVERSE MORTGAGE WITHOUT REDEMPTION RIGHT

We derive in this article the pricing of a reverse mortgage without redemption right. In this, the underlying model employs a jump-diffusion process to represent the dynamics of the housing price, the Vasicek model to drive the instantaneous interest rate, and the force mortality model to describe the longevity risk. The said pricing is based on the Principle of Balance between the expected gain and expected payment. We compute the expected gain and the expected payment respectively under the continuous and discrete framework. We also present, with the above model, explicit formulas for the increasing (or decreasing) perpetual annuity and the level perpetual annuity. Furthermore, we discuss the monotonicity property of the annuities, lump sum, and annuity payment factors with respect to the parameters associated with the house price, the interest rate, and the force of mortality model. Finally, some numerical results for the lump sum, the annuity, and the annuity payment factors are presented, and also the sensitivity with respect to the above parameters is discussed. Based on the average change rate, we evaluate all parameters’ degree of impact on the annuity, the lump sum, and the annuity payment factors.