MODELING LIFETIME EXPECTED CREDIT LOSSES ON BANK LOANS

Abstract

The guidelines of various Accounting Standards require every financial institution to measure lifetime expected credit losses (LECLs) on every instrument, and to determine at each reporting date if there has been a significant increase in credit risk since its inception. This paper models LECLs on bank loans given to a firm that has promised to repay debt at multiple points over the lifetime of the contract. The LECL can be written as a sum of ECLs (estimated at reporting date) incurred at debt repayment times. The ECL at any debt repayment time can be written as a product of the probability of default (PD), the expected value of loss given default and the exposure at default. We derive a stochastic dynamical equation for the value of the firm’s asset by incorporating the dynamics of the factors. Also, we show how the LECL and the term structure of the PD can be estimated by solving a Black–Scholes–Merton like partial differential equation. As an illustration, we present the numerical results for the various credit loss indicators of a fictitious firm when the dynamics of the short-term interest rate is characterized by a Cox–Ingersoll–Ross mean-reverting process.