Volatility modeling is a cornerstone of derivative pricing and risk management. This white paper aims to introduce key concepts in volatility, explore the challenges inherent in volatility calibration, and present an innovative, optimal-transport-based approach developed by genOTC.
From Implied to Local Volatility with Optimal Transport
Volatility modeling plays a central role in the pricing, risk management, and trading of derivatives. Without an accurate understanding of volatility, it becomes difficult to assess the fair value of contracts, design effective hedging strategies, or properly measure exposure to risk. The aim of this white paper is to introduce, in accessible terms for the non-expert reader, some of the foundational concepts behind volatility modeling, highlight the practical and theoretical challenges that arise when calibrating volatility, and present the optimal transport–based methodology developed by genOTC as a breakthrough solution in this space.
Traditional approaches to volatility calibration typically fall into two broad categories: parametric models and interpolation-based methods. While both have been widely applied, neither approach has succeeded in providing a cross-asset, fully robust framework. Parametric models often require complex adjustments or model-specific modifications to capture the nuances of each asset class. Interpolation techniques, though flexible in certain settings, can suffer from inconsistency and instability when extended to different markets or stressed environments.
Volatility calibration is not simply a numerical optimization task. At its heart, it is both a probabilistic and geometric problem, requiring a framework that respects fundamental principles of arbitrage, probability, and market coherence. Optimal Transport offers exactly such a mathematical foundation. By leveraging these insights, genOTC delivers a powerful, scalable solution capable of producing robust, consistent volatility surfaces that are directly applicable to real-world market conditions.
Unlike rigid parametric frameworks, genOTC avoids unnecessary structural assumptions, generating arbitrage-free models that are fully marked to market. This makes it a next-generation tool for mastering volatility, supporting coherent risk management, and enabling all professionals to operate with confidence in increasingly complex financial markets.