Research

CVI (Convex Volatility Interpolation) is a novel approach to constructing and fitting implied volatility surfaces from observed market option prices. Its key innovation lies in reformulating the problem of fitting arbitrage-free volatility surfaces as an approximately convex optimization task. This allows the fitting process to leverage efficient convex solvers, offering both speed and robustness, and bridging the gap between flow and exotics fitters. Specifically, CVI uses a parameterization of the volatility surface in variance space, calibrated using quadratic programming (QP) with linear constraints. Its dual parameterization in cubic spline and B-spline spaces maps a set of intuitive parameters to the weights of basis functions. As CVI has no restrictions on the number of parameters, it can fit any volatility surface. The method works consistently across all underlyings without the need for hyperparameter tuning, relying on dimensionless numbers for the parameterization and fitting logic.