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随着我国人口老龄化程度日益加剧,养老服务需求随之增大,“以房养老”作为新型的养老模式应运而生。反向抵押贷款作为针对老年人可能面临的“房子富人、现金穷人”尴尬而设计出的一种金融创新工具,能否对其进行科学合理定价,是“以房养老”顺利开展的关键。在风险中性条件下,同时考虑房产价值、利率和预期寿命三大主要因素的动态性,创新性地采用借款者向保险公司缴纳保证保险的保费现值等于贷款者向保险公司预期索赔损失的现值,对无赎回权的反向终身年金抵押贷款进行定价,采用CIR模型、LC模型以及跳跃扩散模型分别对利率、死亡率以及房价动态波动性进行拟合。结果显示:借款者可获得的年金额度与其年龄和房屋价值呈正相关关系,与利率呈负相关关系。在对定价结果进行敏感性分析时发现:房价的波动对所支付年金额度的影响最大;在对死亡率进行分析时发现:若忽略借款者死亡率的改善,则支付年金额度将被高估。
With the increasing degree of population aging in our country, the demand for pension services will increase. As a new pension model, “housing for the aged” has come into being. Reverse mortgage loans as a financial innovation tool designed for the embarrassment of older people may face “house rich, cash poor ”, whether it can be scientifically and reasonably priced, is The key to carry out. Considering the dynamics of the three main factors of real estate value, interest rate and life expectancy under risk-neutral conditions, the present value of the premium premium of innovative insurance that the borrower pays the insurance company is equal to the loss of the lender’s expected loss to the insurance company The present value of fixed-price reverse-lifetime pension-backed mortgage is priced. CIR, LC and jump-diffusion models are used to fit interest rate, mortality rate and dynamic volatility of house price respectively. The results show that the amount of annuity available to borrowers is positively correlated with their age and house value, and negatively correlated with interest rates. In the sensitivity analysis of pricing results, we find that the fluctuation of housing prices has the greatest impact on the amount of annuity paid. When analyzing the mortality rate, we find that if we ignore the improvement of borrower mortality rate, the payment of annuity amount will be overestimated.