This study aims to evaluate an insurer's equity during a black swan event by developing a capped call option model. The capped call captures the lending-borrowing relationship by integrating the credit risk from the carbon emission reductions of the carbon-intensive borrowing firm with the insurer's shadow insurance in an imperfectly competitive life insurance market. We show that the borrowing firm invests significantly in green technology, increasing its equity value and the insurer's interest margin, but harms policyholders. Increasing shadow insurance enhances the insurer's interest margin and firm equity. Moreover, we find that stringent cap regulation of the cap-and-trade scheme decreases the insurer's interest margin when the black swan impact becomes significant. This strict cap regulation helps policyholder protection, but harms borrowing firm equity. We suggest that the government shrink the cap of the cap-and-trade scheme, contributing to insurance stability. Colossal black swan increases the insurer's interest margin, policyholder protection, and borrowing firm equity. In conclusion, we show that the capped call option model is relevant to green finance for an insurer-borrowing firm.
