Measuring Provisions for Collateralised Retail Lending

This paper develops a simple model for measuring the provision for a pool of collateralised retail loans with homogenous characteristics (i.e. the same type of collateral and broadly the same loan-to-value ratio) due to default, where the collateral coverage is treated as a put option with the strike price equal to the outstanding loan amount of the pool. The collateral value and the probabilities of default (PD) of borrowers in the pool are the two correlated stochastic variables in the model. Empirical findings based on the data of the residential mortgage market in Hong Kong are consistent with the proposed dynamics of the PD of residential mortgage loans, which reverts to a mean level. The numerical results show that the loan-to-value ratio, correlation between the property price and the PD, volatility of the property price, mean-reverting process of the PD and time horizon are the important factors for measuring provisions. These factors incorporate forward-looking elements, which are however not fully considered in the Basel II framework. The model can be used for assessing whether provisions provided by banks against expected loss are adequate in a forward-looking view, as required by both sound policy and the Banking Ordinance. Promotion of forward-looking provisions with longer time horizons in assessments of risk can also avoid large increases in provisions until the economy is clearly in recession. This means that procyclicality of lending would be reduced to some extent.