Dynamic Model of Credit Risk in Relationship Lending: A Game- theoretic Real Options Approach
We develop a dynamic credit risk model for the case that banks compete to collect their loans from a firm falling in danger of bankruptcy. We apply a game-theoretic real options approach to investigate bank fs 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 non-main bank comes at an earlier stage of 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.
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