Research On The Risk Factors And Pricing Models Of Reverse Mortgage In China

China entered the aging society in the phase of low income, and the aging level of the population speeds up quickly. On the one hand, the fund of current social security is not enough, social dependency ratio is rising, which cannot deal with the increasingly serious aging crisis, on the other hand, due to the emergence of a large number of "four two one city" and "empty nest" family, the traditional family support mode for the elderly is difficult to maintain. Reverse mortgage as a mature financial product innovation, has operated in many foreign countries for many years, which provides a good way to solve the fund shortage problem. Reverse mortgages were conceived as a means to help people in or near retirement and with limited income use the money they have put into their home to pay off debts, cover basic monthly living expenses or pay for health care. Reverse mortgage gets the name because its payback stream is reversed with the traditional mortgage. Instead of making monthly payments to a lender (as with a traditional mortgage), the lender makes payments to the borrower. The borrower is not required to pay back the loan until the home is sold or otherwise vacated. As long as the borrowers live in the home, they are not required to make any monthly payments towards the loan balance.Although the foreign scholars carried out a series of thorough and systematic researches on the reverse mortgage, but our country is in the transition period, the people’s consumption habits, culture, management system, tax and land policies, economic system, the interest rate mechanism, the real estate market situation are quite different compared with the developed countries. There are many obstacles in the operation of reverse mortgage loans, of which the most important content is to reflect and measure the lender and borrower risk factors, and then can make reasonable pricing. Therefore, it is necessary to conduct a specific and in-depth analysis about the main facing risks of the reverse mortgage development in China, from both the qualitative and quantitative aspects. There are two measures of pricing reverse mortgage, including payment factor method and actuarial method. Both of them have certain limitations, therefore, cannot be directly applied in our country. We need to improve the design of pricing model, especially the selection and calculation of the parameters need to be treated carefully, otherwise the calculation results will have a world of difference with real facts, or even larger fallacy. The domestic reverse mortgage pricing research is still in its infancy, the pricing model is more based on static risk assumptions, single or double risk factor fluctuations assumptions, the comprehensive and systematic studies are very few.According to the above research background, we expect to build systems based on system analysis of the development of reverse mortgages facing major risk factors, then build up a pricing system in a comprehensive and reasonable way, to provide effective technical support. The amount of reverse mortgage depends on many risk factors, of which the borrowers’longevity risk, the house value fluctuation and the loan interest rate fluctuation are the three key factors. This paper will investigate how to forecast those factors future wave, then incorporate them into pricing model, to get reasonable pricing results. According to this, four main problems need to be solved in this paper.The first is to identify the main risk factors affecting the reverse mortgage pricing.The second is how to represent the fluctuation pathway of those risk factors, furthermore, how to forecast their future trend.The third one is how to establish the reasonable risk neutral pricing system of reverse mortgage, which can reflect the volatility of main influence factorsThe Fourth one is to do empirical analysis of the pricing model, and test the reasonability.Through doing progressive research on the above four issues, this paper get the following achievements:Firstly, identify the main risk factors of reverse mortgages and analyze them in details, find out the proper measurement models to describe the future fluctuations for main risk factor, and then simulate the future change scenarios of each factor by using the Matlab, Eviews, and Excel software.The second is about the uncertainty of borrower’s future lifetime. This paper points out that with the development of economy and the improvement of living and medical conditions, the average life expectancy in China is prolonging continuously, the mortality rate has been declining and represents the dynamic fluctuation characteristics. Financial institutions should adopt dynamic mortality volatility model to predict the borrower’s future mortality changes. Our research shows that Lee-Carter model is suitable to forecast the mortality trend of China’s population, and in this framework, the future mortality rate of all age groups are estimated by using the experience life table of China’s life insurance industry.The third is about the value fluctuation of borrower’s house. This paper uses the forecasting method of grey system theory; the grey Markov model is built up and conducts a dynamic prediction for house value changes of reverse mortgages by using China’s second-hand housing price index.The fourth is about the loan interest rate fluctuations. This paper points out that China’s interest rate market is under the government control, the reverse mortgage loan interest rate is suitable to using floating interest rate, which should keep the same frequency change with the government loan datum interest rate of more than five years. The pure jump process, which is suitable to describe the Chinese government benchmark interest rate fluctuations, can be used to predict the changes of reverse mortgage rates, and a numerical simulation is conducted by using historical data. In addition, some related risk management suggestions are proposed from the point of pricing and operation.The Fifth aspect is about other risk factors, including adverse selection and moral risk, liquidity risk, policy adjustment, expense risk and value concept. Through qualitative and quantitative analysis, those risks can be controlled effectively by reasonable product design and standardized operation.Sixthly, based on in-depth analysis of the risk factors, as well as the risk neutral financial asset pricing method, this paper constructs a pricing model system with three dynamic parameters. In view of the different payment methods, single or couple applicants, different gender and whether early redemption option included, this paper constructs a series of different pricing models. This paper has collected all kinds of historical data, uses Monte Carlo method to simulate the future scenes of every main factor’s fluctuation in the same time, calculates the empirical pricing results, and carries out the sensitive analysis. All empirical results can be explained reasonably, which verifies the rationality of the pricing system.In the above research achievements, the innovations of this paper are as follows:Firstly, comparison the previous with new experience life tables of China’s life insurance industry shows that the mortality rates have been decreasing significantly, representing the dynamic changing characteristics. Based on the characteristics of the sample data, the author innovatively applies Lee-Carter prediction method to forecast the future mortality of reverse mortgage borrowers, constructs a dynamic mortality volatility model, and does a quantitative analysis of the mortality fluctuations effects of on the reverse mortgage loan pricing.Secondly, because the housing price index is the monthly data, and the time sequence changes relatively stable and represents some volatility, this paper tries to use the Gray Markov Model to fit it. The research conclusion is that Gray Markov Model is a good way to simulate the housing price index, model test results are satisfactory. Therefore, using Grey Markov Model to predict the house value moving trend of reverse mortgage is more consistent with the reality of our country.Third, based on previous reverse mortgage pricing researches, the borrower’s mortality rates are considered as dynamic parameters, this paper establishes innovatively a comprehensive reverse mortgage pricing model system based on3dynamic factors, including interest rates, house value and borrowers’remaining life times. a series of different pricing models are built up in view of the different payment methods, single or couple applicants, different gender and with or without redemption option.Fourthly, this paper points out the understanding biases of previous researchers on the redemption options of reverse mortgage, and redefine it in accordance with the general understanding. This paper points out that the redemption options of reverse mortgage is more suitable to use the pricing and operation methods of American option, furthermore the redemption option pricing models are constructed and the results are calculated.In a word, China’s population aging trend speed up quickly, but the fund of current social security system is insufficient. Reverse mortgage as a financial innovation can fulfill the current pension resources, which is a good way to deal with the aging crisis. Based on in-depth study on the3main risk factors of reverse mortgage, this paper constructs the reverse mortgage comprehensive pricing model system including3dynamic parameters—interest rate, house value and borrowers’ future lifetime, and empirical analyses are also conducted. It is expected to provide some theoretical supports and technical methods to push forward the development of reverse mortgage loan in China.