Modelling Committed Credit Lines

Antonio Castagna

Loan commitments or credit lines are the most popular form of bank lending representing a high percentage of all commercial and industrial loans by domestic banks. Various models exist in the literature for pricing loan commitments: Chava and Jarrow (2008), Jones and Wu (2009) and Bag and Jacobs (2012). These three articles model credit lines by considering many empirical features, but each focuses on only one or some of them, and none offer a complete framework. In fact, Bag and Jacobs allow for partial usage of credit lines, but the authors do not include in the analysis any dependence between default probability and withdrawals; Chava and Jarrow allow for stochastic interest rates and intensity of default, the probability of using credit lines is linked to default probability, but unfortunately (at least in the specified model) partial and multiple withdrawals are not allowed for; finally, Jones and Wu model credit line usage as a function of default probability, with an average deterministic withdrawal that is due to causes other than debtor creditworthiness.

The effects on withdrawals by the default probability, and hence the credit spread of the debtor, is well understood

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