The Construction Of Collateral Loan Pricing Models Under The Reduced-form Approach

Mortgage refers to a party of the contract perform the contract to the other with their own property . When the mortgagor fails to perform the contract,the mortgagee has the right to sale the mortgaged property within the scope permitted by law and seek preferred payments from the proceeds. The Swiss banking sector's loan losses in the mid 1990s of about 40 billion Swiss francs were largely due to a decline of up to 30 percent in the value of properties pledged as collateral. Several factors led to these losses . First , the mortgage loan allocation policy in the 1980s was lax. Most banks for example did not use a formal rating model . Hence , no systematic checks on borrower's creditworthiness existed . Second , no instrument to price the market value of the collateral was in force and clearly , there was no transparency about the interdependence of credit and market risk in the loan portfolios. Third , the economic recession and the unusually high interest rate levels triggered defaults and put houses prices under pressure . 'PRC Security Law' was promulgated in 1996 , the form of assets pledged as a guarantee of economic activity are widely used, the asset-backed funding facility has become the subject of an important activity in the market and the important content of the transactions between a banking and the demand side of funds, mortgage security system has become an important measures to preserve commercial bank assets, prevent credit risks and mitigate the risks .These illustrate that the effective pricing and assessment of collateral is essential for loan pricing and risk management purposes. Collateral is the major means to reduce the credit risk of bank industry .From a borrower's point of view, providing a bank with collateral reduces the cost of a loan, since the bank is willing to compensate him for the reduction in loss due to default. If a borrower defaults , then to a large extent the collateral determines the loss that a bank will incur. Collateral plays an important role in loan pricing.So how to develop an accurate pricing model and to price the collateral loans properly is an important problem that commercial banks have been facing for many years in their business management.Loan pricing is through a comprehensive check of all the interests of the commercial banks from loans , the cost from the corresponding services provided by the commercial banks , the goal income and other factors . The price is made to make sure each loan has market competitiveness , meets the demands of ban's profitability and security.Background of this research is that China's banking sector is promoting the implementation of Basle Committee on Banking Supervision and regulatory authorties's requirements to commercial banks about "in accordance with the principles of risk and return symmetry to determine the risk premium of science,improve the pricing system,improve the pricing calculation".First I make an overview of papers about the effect of collaterals,then through comparing the structural model and reduced form model,we know:(1)Structured models rely on the enterprise value,while the reduce form approach does not require,the analysis has many advantages.(2)Structured method assumes that the enterprise value of events follow a continuous random process,in which case,a sudden drop in enterprise value caused the unpredictable events of default will never occur。Reduce form approach assumes that a time that default occurred is a random variable.At default time, companies immediately jump from the normal state to the default state,reduce form model provides a more realistic and operational approach.(3)reduce form model is more like risk-free bond pricing equation, the only difference is considered the default intensity and default loss rate. Therefore, compared with the structural model, reduce form model is relatively easy to handle in calculation and analysis.(4)The fundamental difference between the two methods rely on their different information set.Structured approach is based on enterprise management information, reduce form method is based on market information.Considering the strengths of Reduced-form approach,I develop some loan pricing models,in which the cash flows of the loan may be single-stage or multi-stages under the assumption of certain environmental in terms of no-arbitrage pricing theory . Finally with some examples demonstrate the application of mortgage pricing model.The innovation of this paper are:(1)the majority of national literatures as the pricing of collateral loans were about house, but collateral pricing in this paper can be used in a variety of mortgage. (2)collateral pricing literatures had many qualifications, such as fixed-rate pricing, prepayment and no default of the mortgage, the pricing formula in this paper can be used calculate loan price in any amount, any time, fixed-rate and floating interest rates, and default can be occurred at any time, so the price is more practical.