Research On Pricing Of Housing Reverse Mortgage With The Stochastic Interest Rate

Our country has entered the stage of aging now.The population of the elderly is constantly increasing,and this situation will not be eased in a short time.Among all kinds of social problems caused by the aging of the population,the first of all is the old-age problem of the elderly.For family,there will be more and more "421" and "empty nest" families in our country,and the traditional family pension model no longer applies.For the society,with the increase of the number of the elderly,it is bound to bring more financial pressure to the existing social security system,and the social pension system does not always guarantee the pension problem for all the elderly.Reverse mortgage,as a product that has operated for many years abroad,provides a viable solution to alleviating the growing problem of pension in China.The key to the success of reverse mortgage is a reasonable pricing.Therefore,this article focuses on the pricing of reverse mortgage under stochastic interest rates.This paper mainly discusses the following aspects:First of all,this paper describes briefly the background of the study,the degree of population aging in China,and the trend of future aging.Then the significance of this study and the current situation of domestic and foreign research are expounded.In addition,the article also made a simple comb on the context of the framework.Secondly,this article introduces the concept of reverse mortgage,and introduces three kinds of pricing methods for housing reverse mortgages,payment factor pricing method,option pricing method,and actuarial pricing method.Then it introduces relevant theories including interest theory,survival model,Monte Carlo simulation and so on,which provides theoretical basis for the follow-up work of the paper.Thirdly,the interest rate is randomized and the interest rate is assumed to be subject to Vasicek interest rate model.Using the option function of the generalized moment estimation method in Eviews8 software,the Vasicek model parameters are estimated with the data of seven days repurchase rate between banks.Similarly,assuming that the price fluctuation satisfies the geometric Brownian motion,the parameter of the price fluctuation model is estimated by using the option function of the generalized moment estimation method in the Eviews8 software and combining the selected house price data.Then this paper introduces a fixed-rate housing reverse mortgage pricing model,in the fixed interest rate of housing reverse mortgage pricing model after the correction,and puts forward a stochastic interest rate of housing reverse mortgage pricing model and stochastic interest rate under the price of housing reverse mortgage pricing model.Finally,this paper uses Matlab to simulate the housing reverse mortgage pricing model.Based on the fixed interest rate,random interest rate,and random interest rate based on volatility house prices,the reverse mortgage ledger amount and the annuity claim amount were calculated respectively for the single-life state and dual-life state.At the same time,the sensitivity of the parameters in the above three pricing models was analyzed.Through comparative analysis,it is concluded that the housing reverse mortgage based on random interest rate is more attractive to the elderly and helps improve the quality of life of the elderly.