Actuarial Pricing Models Of Reverse Mortgage With The Stochastic Interest Rate

The aging problem became more important and serious in China in recent years, and pension for the senior citizen lacks. The traditional supporting model for the aged by families has converted to multiple models, such as social aged-care model and self-help model. The reverse mortgage is a creative measure to support the aged people. However, whether the reverse mortgage and its relative products could be implemented in China depend on their reasonable pricing. The pricing of the reverse mortgage is affected by many factors, i.e. the house value, expected residual life and loan interest rate, which is stochastic and fluctuating with economy and policies of the country. In this paper, actuarial pricing models of reverse mortgage with the stochastic interest rate were established.Firstly, at the fixed interest rate, the traditional basic actuarial pricing model of reverse mortgage was improved, and pricing models for single-life and double-lives with interest,which is calculated by continuous mode, were established. Meanwhile, to reduce the inflationary risk, linear increasing annuity and equal ratio increasing annuity actuarial pricing models for single-life and double-lives with interest, which is calculated by continuous mode,were built. Using these models could reduce the errors caused by impractical and imprecise assumptions in previous researches.Secondly, to solve the problem that the traditional basic actuarial pricing model only could be calculated by the fixed interest rate, standard Wiener process and negative-binomial distribution united built the accumulation function of interest force, which were employed to establish the models for single-life and double-lives, including a lump sum pricing model,annuity pricing model, linear increasing annuity and equal ratio increasing annuity pricing models at the stochastic interest rate.Thirdly, in order to analyze the models using experiential mortality table, a assumption for the age at death was given, and then at the fixed interest rate and the stochastic interest rate, a lump sum pricing model, annuity pricing model, linear increasing annuity and equal ratio increasing annuity pricing models were given for single-life and double-lives with the UDD assumption.Fourthly, in the numerical simulation, the initial values of parameters were set up by collecting data, and Matlab was used to calculate the pricing models with the UDD assumption. The results showed that the loan values of the UDD models were higher than that of pricing models with the fixed interest rate, that is the UDD models would be more attractive to borrowers. The analysis of sensitivity to parameter for the models with the fixed interest rate indicated that the interest rate was more sensitive than average growth rate and depreciation rate of the house value. The influence on the loan due to the change of different parameters for the actuarial pricing models under stochastic interest rate, state that the constructed models conforms to the actual situation and has extensive practical application value.