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Parameter identifiability and uncertainty reports #25
SVI parameters can be poorly identified while the fitted smile is excellent: near-indistinguishable smiles from very different (a,b,rho,m,sigma). Stable fitted IV is not stable fitted parameters -- signals built on parameter changes can be pure optimizer noise.
Proposal
Per-fit identifiability tooling:
fit.jacobian() (dw/dtheta at the quotes), fit.condition_number()
fit.parameter_uncertainty() -- covariance from the Gauss-Newton approximation at the optimum (residual-scaled), reported as per-parameter standard errors and correlations
fit.identifiability_report() -- a formatted block flagging well/poorly identified directions (e.g. sigma-b correlation, wing under-determination on narrow strike ranges)
Builds on the analytic derivative kernels; ties into the fit-report wrapper.
Acceptance criteria
Narrow-strike fixture flags wing parameters as poorly identified while iv RMSE is tiny
Uncertainties shrink as the strike range widens
Works for the SVI family analytically; FD fallback elsewhere
Activity