Black-Cox Model

Private Credit Glossary

Extension of the Merton structural credit model (1976) that introduces a default barrier K: default is triggered the first time asset value crosses K rather than only at maturity. The covenant is modeled as a down-and-in option whose first-passage time has a closed-form distribution under geometric Brownian motion. The Black-Cox spread is lower than the Merton spread for the same leverage because early triggering preserves recovery value: Covenant Value = s_Merton - s_Black-Cox, empirically about 80–120 bps for typical unitranche loans at 5–6× leverage.

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