Convex Volatility Interpolation (CVI) for Options Pricing | Risk.net

Fast, accurate, and arbitrage-free volatility surface fitting remains a core challenge for options desks, with a new framework offering a potential solution. Fabrice Deschâtres has introduced Convex Volatility Interpolation (CVI), a method that frames the problem as quadratic programming in variance space.

CVI aims to address the difficulties in generating volatility surfaces that can precisely fit market conditions while avoiding arbitrage opportunities. According to Deschâtres, the approach utilizes intuitive parameters, incorporates bid-ask spread awareness through penalties, and provides a rigorous treatment of volatility tails.

Deschâtres highlighted the distinction between CVI and SANOS, another approach to constructing volatility surfaces. While both rely on convex optimization for global calibration and can accommodate flexible parameterization, SANOS operates in price space, while CVI operates in variance space. The choice of variance space, Deschâtres argues, allows for more trader-friendly parameters and a better capture of the volatility surface’s shape – level, skew, and curvature – key properties for practical application.

The development of CVI builds on a broader trend toward convex optimization in volatility fitting, a technique Deschâtres describes as the “only sensible choice” for handling the large number of parameters involved. He notes that achieving a volatility surface free of calendar spread and butterfly arbitrage, while simultaneously fitting bid/ask spreads and allowing for regularization, is a complex undertaking.

Deschâtres previously discussed the challenges of generating arbitrage-free volatility surfaces in a November 2022 LinkedIn post, noting that, to his knowledge, no publicly available paper fully solves the problem, with Voladynamics being a key reference point in the field. He emphasized the necessitate for constraints to prevent arbitrage and an objective function that incorporates market fitting and regularization.

In a related post from January 2026, Deschâtres compared SANOS and CVI, noting that SANOS’s operation in price space structurally simplifies the enforcement of strike arbitrage constraints. He also indicated a willingness to discuss volatility fitting solutions with teams evaluating options for trading, risk management, and valuation purposes.