Driolkyovricnotfysne

The SVI parametrization offers a tractable and no-arbitrage-consistent representation of the implied volatility smile at a fixed expiry. Calibrating it to observable market data is more nuanced than the elegance of the functional form suggests.

The SVI model represents the implied variance smile as a function of log-moneyness using five parameters — the level, slope, curvature, and two parameters governing the rotation and translation of the smile shape. In theory, a surface constructed from SVI slices at each expiry is free of butterfly arbitrage by construction. In practice, fitting the model to noisy market quotations introduces calibration instability, particularly in the wings where option liquidity thins and bid-offer spreads widen relative to the mid-price the calibration routine targets.

Before initiating any numerical calibration, the raw implied volatility surface extracted from observable option prices should be cleaned for obvious data artefacts — prices that violate put-call parity, quotations with zero open interest in illiquid strikes, and points where the bid-offer spread is so wide that the mid-price carries minimal informational content. Calibrating SVI to uncleaned surface data produces parameter estimates that fit noise rather than signal, and the resulting smile representation will typically fail basic smoothness checks in the wings.

The choice of initial parameter values materially affects the convergence behaviour of the optimisation routine. A common approach is to seed the level parameter from the at-the-money implied volatility, the slope from the observed skew gradient around the money, and the curvature from the butterfly spread level at a defined moneyness offset. These heuristic starting points do not guarantee convergence to a globally optimal solution, but they substantially reduce the risk of the optimiser settling in a local minimum that produces a poor smile representation in one or more surface regions.

Once calibrated, the quality of the SVI fit should be assessed not only by the aggregate root-mean-squared fitting error across all strikes but also by visual inspection of the residuals across the moneyness range. Systematic residual patterns — consistent overpricing of the downside wing or underpricing of near-the-money implied volatility — indicate that the SVI functional form is misspecified for the surface being fitted, and that a richer parametric form or a non-parametric interpolation method may be more appropriate for that expiry and market condition.