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Implied Volatility Surface Construction L1-442

Computational FinanceVolatility modelingδ=3 · standardL_DAG = 3📋 Stub — not mineable
📋

Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

Forward model E

\sigma_impl(k, T) modeled by SVI parameterization: w(k) = a + b\cdot (rho\cdot (k-m) + \sqrt{(k-m) \cdot \cdot 2 + \sigma \cdot \cdot 2))

Implied Volatility Surface Construction: Implied vol surface construction: build smooth, arbitrage-free implied volatility surface from sparse market quotes. The forward operator produces the measurement through a 3-node primitive DAG (S.interpolation.cubic_spline…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=3 with effective condition number kappa_eff~30; sparse_data_interpolation_error, butterfly_arbitrage_violation set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.

L-DAG

S.interpolation.cubic_spline -> N.pointwise -> O.svi.calibration
S.interpolation.cubic_splineN.pointwiseO.svi.calibration

Well-posedness W

Existence:
true
Uniqueness:
true
Stability:
conditional
κ:
500

Existence of the recovered implied_vol_surface 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 ~= 30); sparse_data_interpolation_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market bid ask gaussian sets the irreducible data-fidelity floor.

Solvability C

Solver class:
classical [SVI_SSVI_calibration or parametric_surface_fit]
Convergence rate q:
2
Complexity:
O(N_slices * N_params_SVI) per calibration per iteration

Specs (0)

No L2 specs registered yet for this principle.