Default probability of a captive credit bank with government capital injections: A capped barrier option approach

Auto dealers use floorplan financing to buy cars from the original equipment manufacturer (OEM) with credit typically provided by the OEM's captive credit bank. The purpose of this paper is to explicate and model captive bank lending to dealers and determine the loan-risk default probability in equity returns of the captive bank under government capital injections during a financial crisis. The lending function of the captive bank necessitates modeling equity return as a “capped” barrier option. Numerical exercises show that a decrease in the discount rate of the floorplan financing or an increase in the amount of government capital injection decreases the default probability in equity returns of the captive bank. Floorplan or government assistance enables the captive bank to be much less prone to loan risk, specifically with large-scale dealers which can substantially affect the stability of the banking system.