Merton Credit Risk Structural Model L1-443
Unclaimed Principle — open for contribution
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Forward model E
Merton Credit Risk Structural Model: Merton model: recover firm asset value V and asset volatility sigma_V from equity market cap and equity volatility. The forward operator produces the measurement through a 3-node primitive DAG (M.merton.structural…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=5 with effective condition number kappa_eff~80; debt_complexity_multiple_tranches, default_boundary_uncertainty set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 2000
Existence of the recovered firm_value_vol_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); debt_complexity_multiple_tranches dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market gaussian sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- classical [Newton_2eq_system or iterative_MLE (Duan 1994)]
- Convergence rate q:
- 2
- Complexity:
- O(N_firms * N_iter_Newton) for portfolio per iteration