SANOS: Smooth strictly Arbitrage-free Non-parametric Option Surfaces

Battle Count: 50

Extremely relevant to quantitative trading. The method provides a fast (sub-one second), smooth, strictly arbitrage-free option surface that can be used directly in trading systems. It is specifically designed for high-speed trading environments and ML-based strategies like Deep Hedging. The ability to fit within bid-ask spreads, handle 0DTE to long-dated options, and avoid the 'too expensive' problem of linear interpolation makes it directly applicable to market making, option pricing, and risk management. The positivity-only parametrization is ideal for generative models and gradient-based optimization in trading pipelines.

The production model is relatively simple: it reduces to solving a single global linear program with linear constraints (non-negativity, unit mean, unit expectation, martingale condition). The matrices are pre-computable. The toy model has quadratic execution time but the production model handles inhomogeneous grids efficiently. The generalized model (Theorem 3.9) is significantly more complex due to tensor structures. Overall, the core method is accessible to anyone familiar with linear programming and Black-Scholes pricing, though careful handling of strike grids, variance interpolation, and bid-ask constraints requires attention.

The paper provides detailed mathematical formulations, linear program specifications, and implementation strategies. Data is sourced from OptionMetrics IvyDB (commercial, not freely available). No GitHub repository is explicitly mentioned. The algorithmic structure is well-described with explicit matrices and constraints, but full code is not provided. The toy model in Section 4.1 aids understanding but is noted as not production-ready.