SANOS Smooth strictly Arbitrage-free Non-parametric Option Surfaces

2026-01-16

AI Summary

This study addresses the challenge of constructing option price surfaces that are simultaneously smooth and strictly arbitrage-free across both time-to-maturity and strike dimensions. To this end, the authors propose an efficient and flexible nonparametric method that directly calibrates to market quotes via linear programming, ensuring smoothness and absence of arbitrage under only simple positivity constraints, while naturally accommodating bid–ask spread bounds. The key innovation lies in the introduction of an equivalent parametrization in terms of positive “discrete local volatility,” which substantially simplifies the constraint structure. Compared to existing approaches that fit implied volatility surfaces, the proposed method significantly reduces computational cost and demonstrates strong empirical performance and practicality when applied to S&P 500 index option data.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning with Manifolds
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitrage-free across time and strike. The method can be viewed as a smooth generalization of the widely-known linear interpolation scheme, and retains the simplicity and transparency of that baseline. Calibration of the model to observed market quotes is formulated as a linear program, allowing bid-ask spreads to be incorporated directly via linear penalties or inequalities, and delivering materially lower computational cost than most of the currently available implied-volatility surface fitting routines. As a further contribution, we derive an equivalent parameterization of the proposed surface in terms of strictly positive"discrete local volatility"variables. This yields, to our knowledge, the first construction of smooth, strictly arbitrage-free option price surfaces while requiring only trivial parameter constraints (positivity). We illustrate the approach using S&P 500 index options

Problem

• option price surfaces
• smoothness
• arbitrage-free
• non-parametric
• calibration

Innovation

• arbitrage-free
• non-parametric
• option surface
• discrete local volatility
• linear programming