A Forecasting Model for the Likelihood of Delinquency, Default or Prepayment: The Case of Taiwan

ABSTRACT In a competitive and dynamic market, financial institutions must forecast the proportion of mortgages that will become delinquent, default or prepay. This paper develops a novel forecasting model with nonstationary Markov chain and Grey forecasting, capable of predicting the likelihood of delinquency, default and prepayment. Home mortgage data, obtained by a major Taiwan financial institution from January 1, 1996 to June 30, 1998, are adopted to examine the forecasting effectiveness of the novel forecasting model and the ARIMA model. Empirical results indicate that the novel forecasting model with a low error is better than ARIMA. Thus, the novel forecasting model provides a promising means of accurately predicting the probabilities of delinquency, default and prepayment. JEL: C60, G2, G21, 053 Keywords: Forecasting; Mortgage; Loan; Delinquency; Default; Prepayment I. INTRODUCTION The home mortgage sector is critical to financial institutions. However, delinquency, default and prepayment of home mortgages make regulating funds difficult for financial institutions. Managers in the home mortgage sector require the ability to forecast the proportion of mortgages that will be delinquent, defaulted or prepaid. Many methods have been used to forecast delinquency, default or prepayment. For example, Standard \u0026 Poors (SP Smith and Lawrence, 1995) and neural networks (Altman, Marco and Uaretto, 1994). Meanwhile, Merton (1974) employed an option-theoretic approach to default risk. Migration analysis is the most interesting. Researchers have typically used Markov chains to perform migration analysis. Cyert, Davidson and Thompson (1962) applied stationary Markov chains to model credit accounts. However, the suitability of the stationary Markov chain remains unproven. Smith and Lawrence (1995) considered a dynamic environment and constructed a forecasting model with a Markovian structure and non-stationary transition probabilities. The forecasting model is structured as a mathematical recursion to predict the probability of a loan\u0027s being in any one of the alternative financial states annually. The calculation process is too complex to understand. Neither Cyert etc. (1962) nor Smith and Lawrence (1995) predict the probability of delinquent payment and prepayment. Smith and Lawrence (1995, 1996) also forecast losses at annual intervals, but such information is not sought by financial institutions. In a competitive and dynamic market, financial institutions must be able to predict the situation over the forthcoming months. However, previous studies have not considered this fact. The above methods typically require many data to build the forecasting model. However, Taiwan\u0027s financial institutions normally lack such a complete database. Grey forecasting does not depend on a large amount of data. Grey forecasting is fit for Taiwan\u0027s and other financial institutions, which possess insufficient data. Furthermore, Xu and Wen (1997) applied grey forecasting to forecast accurately the passengers of international air transportation. Yi (1987) used grey forecasting to predict the number of talented persons. Their results illustrated the ability of grey forecasting to deal effectively with incomplete or uncertain information. Accordingly, this paper constructs a forecasting model with nonstationary Markov chain and grey forecasting, to forecast the likelihood of delinquency, default and prepayment of home mortgages on a monthly basis. The method can mitigate the difficulties in home mortgage risk management, facilitate financial institutions\u0027 controlling of funds, and help to establish appropriate reserves to protect against losses. …