Mechanism Research On Risk Pricing Model Reverse Mortgage

As China enters into an aging society, the current retirement pension system and traditional way of family support for the aged have been insufficient to deal with the aging crisis. It is urgent to find a new way to support the old people. As a financial innovation, reverse mortgage can be a good solution to the problem. The key to reverse mortgage being successfully put into practice in China lies in a proper way to price the product, which concerns the motivation of both the lender and the borrower. If this problem can be solved, it would be very meaningful for the implementation of reverse mortgage in China.However, the two main pricing models abroad, "Pay Factor" and "Insurance Actuaries", both have their limitations if used directly in China, since the house price and interest rate fluctuations are different in Chinese market. And there are still no comprehensive researches about its pricing in the existing domestic researches.Based on the above practical and theoretical backgrounds, this paper's task is to build a pricing system for reverse mortgage in a comprehensive way, in order to provide related technical support. The pricing of reverse mortgage is deciding the loan amount the borrower can get from the lender. This amount depends on a lot of factors, of which the loan interest rate, the house value and the remaining life of the borrower are the most important. This paper will mainly investigate in how to properly incorporate those three risk factors into the pricing model, to get more reasonable pricing results.To address this issue, this paper first analyzes three kinds of risk pricing methods, risk-adjusted discount factor method, certainty equivalent method and risk-neutral pricing method, in details. Then it points out that, the exsiting models mainly use risk-adjusted discount factor method, such as "Pay Factor" and "Insurance Actuaries", etc. However, since reverse mortgage products don't have homogeneity and the main factors of pricing are quite descriptive, the "risk-neutral pricing" method would be the best for the pricing of reverse mortgage.On the basis of this, this paper innovatively brings up the idea of using the risk-neutral pricing method to build a complete pricing system for reverse mortgage with thorough discussion of the three main risk factors, which contributes to four crucial sub-topics of the paper:First is how to construct the risk-neutral pricing system reverse mortgage;Second is how to reflect the risk of interest rate fluctuations in the pricing model;Third is how to reflect the risk of house price fluctuations in the pricing model;Forth is how to reflect the uncertainty of the borrower's remaining life in the pricing model;After doing progressive research into those four sub topics, this paper's main research achievements are as follows:Firstly, the idea of risk-neutral pricing method for reverse mortgage is like this: First is to build basic formulae to reflect the inter-relations of all the factors using the principles of asset pricing; Next is to analyze three main risk factors in depth to find a best econometric model for describing the future fluctuations of the factors; And finally, we can get the pricing results using numeric method through simulating the scenarios where all three factors change simultaneously.Secondly, about the loan interest rate fluctuations, this paper's main creative point is that reverse mortgage would be skipping floating-rate loans based on the government rate in China, therefore the simple jumping process of the government rates should be used to describe the reverse mortgage interest rate.Thirdly, about the house value fluctuations, this paper points out that, whether to use lognormal random walk process or ARMA model depends on the stationary of time series, according to formal researches. Then a random model is estimated for the data of Shanghai using Eviews.Fourthly, about the uncertainty of the borrower's remaining life, actuarial principles are used to calculate the probability distribution of the remaining life. And this paper studies about two different situations:single borrower and double borrowers.Fifthly, on the basis of the above discussion, the final risk-neutral pricing system of reverse mortgage is constructed and typical data are used to do empirical numeric pricing and sensitivity analysis through Monte Carlo simulation in MATLAB. The pricing results can be explained well, which proves the reasonability of the risk-neutral pricing system of this paper in return, also provides sound theoretical base of product pricing for reverse mortgage's future implementation in China.And finally, with the financial crisis still catching people's eyes, this paper discusses briefly about several possible ways to take precautions against the pricing and operation risks of reverse mortgage.The main creative points of the above research achievements are:Firstly, this paper is the first to raise the idea of using risk-neutral pricing method for reverse mortgage, and also the first paper which has constructed such a complete pricing system with comprehensive understanding of three main risk factors.Secondly, reverse mortgage is categorized as "with redemption right" and "without redemption right" in the formal researches, and they are priced separately in different ways. This paper innovatively brings up the idea of stripping out the redemption right and pricing it separately. Then corresponding models are built up.Thirdly, this paper's another main creative point is that reverse mortgage would be skipping floating-rate loans based on the government rate in China, therefore the simple jumping process of the government rates should be used to describe the reverse mortgage interest rate. In this way, the pricing system would be more reasonable considering the realistic situations in China.In a word, this paper mainly investigates in how to properly price reverse mortgage-a financial innovation to fulfill the house-for-pension scheme, based on the background that the current retirement pension system and traditional way of family support for the aged have been insufficient to deal with the aging crisis in China, which has both practical significance and theoretical value to some extent. Pricing is the key to reverse mortgage being successfully put into practice, and this paper provides sound theoretical base of product pricing for reverse mortgage's future implementation in China through progressive research into the risk-neutral pricing system.