= Merton model
{c}
{title2=$D_T=\min(V_T,F),\quad E_T=(V_T-F)^+$}
{wiki}
In the basic structural model, the firm's asset value $V$ follows <geometric Brownian motion> with constant volatility and a single debt obligation of face value $F$ matures at $T$. <Default> at maturity occurs when $V_T<F$. Equity is a call on firm assets; debt is the risk-free face claim minus a put on those assets, since $\min(V_T,F)=F-(F-V_T)^+$. This links debt valuation to asset value, volatility and capital structure. The basic model does not permit <default> before maturity; richer structural models add a <default> barrier or more detailed obligations.
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