| Since the family planning has been implemented for31years, the birth rate of our country is declining gradually. At the same time, with the rapid economic development and the improvement of medical standard of our country, the average life expectancy of our population has gradually extended. According to the data released by the bureau of statistics of China about the detailed summary data calculation of the6th national census of population, the average life expectancy become higher and higher. In our country the trend of population aging will be increasingly serious. At present, our country is still a developing country. Due to the existence of a series of problems, which including the low standard of economy, national finance income and average per capita income, the impaction of the social security system,and the pension gap, the supporting problem of the aged has become one of China’s current problems to be solved imminently. One case that can’t be ignored is that aging has become quite a serious problem all over the world. Experts and scholars at home and abroad developed the reverse mortgage. The reverse mortgage originated in the Holland, then was introduced to the United States. It is a new type pension products which the housing owners mortgage their own houses to the bank, insurance company or other financial institutions to get loans to pay for the daily life of the old. As a supplement of social endowment, it does good to solve the pension problem of some western developed country, improve the residents’ consumption ability, and active real estate market in practice.In this paper, the author use the theory of profit and loss balance principle and the option pricing model to price the reverse mortgage. The author integrates the longevity risk which is also the cross risk faced by the lender to the base of the option pricing model. On lenders’ profit and loss balance, pension’s actuarial present value that the lender pay the borrower must not less than the value’s actuarial present value that the lender can take back when the reverse mortgage contract expires. The first part of this article expounds the highlight of the pension problem in our country at present stage, and four of our current pension model support, including raising children, providing for social security pension, pension and commercial endowment insurance, and it also put forward the concept of "retirement with house" as well as its theoretical and practical significance for the first time. The second part of this article not only briefly introduces the definition of reverse mortgage and the similarities and differences it shares with the traditional housing mortgage products, but also analyzes the two new financial products comparatively. Then according to the development of reverse mortgage and the actual operation situation both at home and abroad, the article analyzes the difficulties of the implementation of housing reverse mortgage loan insurance product is facing. The third part simply analyzes the risks that faced by lender and borrower of the reverse mortgage, including interest rate risk, longevity risk, house price volatility risk and adverse selection and moral hazard. The fourth part of the article reviews the housing reverse mortgage loan pricing method and the research status at home and abroad. According to whether the borrower have right to own property mortgage when the reverse mortgage contract expires, the reverse mortgage is divided into reverse mortgage without right of redemption and with right of redemption. The fifth part of the article is a key part of the article. It firstly introduces the definition and classification of options and Black-Scholes option pricing theory. Then according to whether borrower have the right to own property mortgage, the housing reverse mortgage loan insurance is divided into housing reverse mortgage loan without right of redemption and with right of redemption. The author obtained the one-time pay pension credits and payments in the form of an annuity pension that lender should give to borrower with the help of option pricing theory in the financial markets, and do pricing analysis on the reverse mortgage with right of redemption based on the borrower’s profit and loss balance equation. Then, this paper respectively analyzed longevity risk to the lender pension payment amount in the two forms of the borrower’s death time obey the continuous and discrete. Finally, the author collected the data of the commodity housing sales prices in Chang De city, Hunan province and the domestic financial market interest rate in the past10years, and then use the data to verify the rationality and feasibility of the model. On the basis of the above, t he author uses the law of control variable initial to empirically analyze each of the parameters in the model results including house prices, house prices expected growth rate and house price volatility, the borrower’s life, loan contract interest rate, the risk-free interest rate, the borrower’s death probability, the correlation coefficient between different borrowers and the sensitivity that the number of people participate in housing reverse mortgage loan to the annuity payment amount of the lender.Under the big boom of "retirement with house", this paper make the shallow analysis about the reverse mortgage. The main contribution has the following three aspects:First, the paper’s research content conform to our country’s basic national conditions nowadays. With the highlight of ageing problem, pension problem has become one of the important problems to be solved in our country. The state council launched the "retirement with house" file in2013to implemented the reverse mortgage in the coastal city of pilot. The research can provide theoretical reference for it. Second, the author obtained the N homogeneous risk of the borrower’s house prices expected rate of growth and volatility on the basis of a large number of domestic and foreign literature, using the law of large Numbers and central limit theorem in actuarial theory. Then the author integrate the longevity risk with the option pricing model to price the reverse mortgage, which is also this article’s innovation point lies in. The author uses the mathematical software to make the empirical analysis of the model parameters and the sensitivity of the pension payment amount on the basis of mathematical model, which greatly strengthen the theoretical pricing model’s practicality, and play a certain role in promoting our country to launch similar financial insurance products in the future. |
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