Measuring Provisions for Collateralised Retail Lending

This paper develops a simple model based on an options approach to measure provisions covering expected losses of collateralised retail lending due to default. The dynamics of the probability of default of retail loans is allowed to follow a meanreverting random process, which captures the characteristics of an economic cycle. Based on the data of the residential mortgage market in Hong Kong, the proposed dynamics of the probability of default is consistent with the empirical findings. A closed-form formula of the model is derived and used to calculate the required provision for a pool of retail loans with the same type of collateral. The numerical results show that the loan-to-value ratio, correlation between the collateral value and the probability of default of borrowers in the pool, volatility of the collateral value, mean-reverting process of the probability of default and time horizon are the important factors for measuring provisions. As the parameters associated with these factors are in general available in banks’ databases of their retail loan portfolios, the model could be a useful quantitative tool for measuring provisions. JEL Classification: C60, G13, G28