WSVI: A Dimensionless Shape Family for Implied Volatility and Its Static No-Arbitrage Structure

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Highly relevant for options market-making, volatility surface calibration, and risk management. W-shaped smiles around binary events (earnings, central bank decisions) are common in practice, and the inability of eSSVI to capture them is a real limitation. The static no-arbitrage conditions (butterfly, spread, calendar) are directly applicable to trading desk risk checks. The closed-form derivatives enable efficient Greeks computation. However, the paper is theoretical and does not provide a calibration algorithm or empirical performance comparison, limiting immediate practical deployment.

The parametric form is closed-form and analytically differentiable, which is favorable. However, implementation requires: (1) careful handling of the basis functions phi_j with their scales, orders, and sides; (2) evaluation of the recursive derivative formulas (Proposition 2.10-2.11) with special treatment for n=1; (3) enforcement of the domain condition c >= delta_c > 0; (4) pointwise checking of butterfly (g >= 0), spread (0 <= C <= 1), and calendar conditions; (5) selection of basis member parameters. The nesting property (Proposition 2.13) simplifies model selection. No code is provided.

The paper provides complete closed-form mathematical expressions for the WSVI family, its derivatives, domain conditions, and no-arbitrage constraints. All formulas are explicitly stated (Equations 1.1, 2.6-2.9, 2.14, 2.24, 4.1-4.20). However, no code, calibration procedure, or numerical implementation is provided. The authors mention a separate forthcoming manuscript on calibration. The theoretical framework is fully self-contained and reproducible from the equations alone.