A barrier option that activates only when the underlying asset's value crosses below a specified barrier K. In Black-Cox credit theory, a financial covenant is modeled as a down-and-in option held by the lender: the right to intervene (accelerate, extract concessions, or force a restructuring) springs into effect the first time the borrower's asset value V_t touches K — the first-passage time of V_t under geometric Brownian motion has a known closed-form distribution.