Simplifying the valuation of reverse annuity mortgages

Abstract

This research derives an approximate pricing formula for valuing reverse annuity mortgages that allows house prices and interest rates to be stochastic. Our approximation approach reduces computational intensity, because it only requires an expectation (average) and a variance of the termination time. We compare the results from our approximate pricing formula with results from simulations and find that the formula provides a close approximation to the simulation results. We conclude that these approximating formulae are useful in valuing and hedging reverse mortgage portfolios, whereas simulations are computationally prohibitive. We further note that the difference between the results of the approximation formula and the simulation is small and generally less than 1%.