Pricing Of Housing Reverse Mortgage Under Stochastic Dynamic Mortality

According to the National Bureau of Statistics,the aging population in China presents the following characteristics: accelerated aging speed,getting old before getting rich,imbalanced development among regions,and a huge number of the elderly living alone in empty nests.Housing reverse mortgage was piloted in China in 2014 and officially promoted nationwide in 2018 as an effective tool to relieve the pressure of social endowment and cope with the aging population in China.However,after nearly six years of market promotion,the reverse mortgage market in China is still a "niche market" compared with those abroad.Many scholars point out that unreasonable pricing,purely commercial operation,traditional Chinese concepts and similar product design are holding back the development of China’s reverse housing mortgage market.Among these factors,reasonable pricing is the key to the success of housing reverse mortgage.As one of the important factors in housing reverse mortgage pricing,the accurate prediction of population survival probability is directly related to the rationality of product pricing.At present,the static survival probability of life table is mostly adopted,while the temporal dynamics of mortality data is neglected.Therefore,this paper mainly focuses on the research of housing reverse mortgage pricingbased on stochastic dynamic mortality model.Firstly,this paper briefly introduces the research background and concepts,risk management and theoretical research related to housing reverse mortgage,which provide theoretical basis for this paper.Secondly,it compares and analyzes six stochastic dynamic mortality models from qualitative and quantitative indicators to determine which is the most suitable one for elderly Chinese population.According to the imitative effect,forecasting performance,stability and biological rationality,CBD model is selected as the most suitable stochastic dynamic mortality model for China.Thirdly,this paper makes an empirical analysis of housing reverse mortgage pricing based on stochastic dynamic mortality model.Finally,under the condition of insufficient demand for current housing reverse mortgage,it puts forward and makes an empirical analysis of the pricing of housing reverse mortgage based on stochastic dynamic mortality model with additional European options or long-term care insurance function.By means of model construction,numerical analysis,empirical analysis,etc.,this paper has established the pricing of housing reverse mortgage based on stochastic dynamic mortality model,which is expected to be of theoretical and practical values for promoting the development of housing reverse mortgage in China.This paper draws the following conclusions: first,in the study of stochastic dynamic mortalitymodel,no single model can perform well in all criteria.Based on the comparative analysis of a variety of indicators,it is concluded that CBD model is the most suitable stochastic dynamic mortality model for mortality data of male and female between the ages of 50 and 89 years old in China.Second,the introduction of reverse housing mortgage can effectively increase the endowment reserve for the elderly population and significantly improve the quality of life of the elderly in their later years.But the choice of mortality factors will change the annuity and lump-sum loan income of the elderly population.In comparison,stochastic dynamic mortality model can more effectively alleviate the basis risk caused by longevity risk,which makes the pricing of this product more reasonable.Third,the income the borrower can obtain is negatively correlated with the borrower’s age,loan interest rate,depreciation rate,expense ratio and other factors,and positively correlated with the value of the house.Lenders should set specific prices based on the gender and health status of the borrower,depreciation of the house and other aspects.Since the life expectancy of female population is generally higher than that of male population,the product should be priced strictly according to gender.Fourth,in terms of sensitivity significance,housing reverse mortgage is the most sensitive to housing price fluctuations,followed in turn by interest rate volatility,housing depreciation,and expense ratio and long-term care expense factors.In addition,female borrowers are moresensitive to various factors than male borrowers.To sum up,the government should give full play to the dominant position of the housing reverse mortgage market,lenders should choose appropriate mortality model for housing reverse mortgage loan pricing,lending institutions in the housing reverse mortgage loan pricing should strictly manage longevity risk,price volatility risk and interest rate risk,strengthen the risk management of the product.Finally,government and professional organizations should actively design diversified products to increase and stimulate people’s demand.