We develop a dynamic credit risk model for the case in which banks compete to collect their loans from a firm in danger of bankruptcy. We apply a game-theoretic real options approach to investigate banks’ optimal strategies. Our model reveals that the bank with the larger loan amount, namely, the main bank, provides an additional loan to support the deteriorating firm when the other bank collects its loan. This suggests that there exists rational forbearance lending by the main bank. Comparative statics show that as the liquidation value is lower, the optimal exit timing for the nonmain bank comes at an earlier stage in the business downturn and the optimal liquidation timing by the main bank is delayed further. As the interest rate of the loan is lower, the optimal exit timing for the non-main bank comes earlier. These analyses are consistent with the forbearance lending and exposure concentration of main banks observed in Japan.
Keywords: Credit risk; Relationship lending; Real option; Game theory; Concentration risk
Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.