DYSANOS Generative Dynamic Smooth Arbitrage-free Non-parametric Option Surfaces

arXiv:2608.12587v2 Announce Type: replace-cross Abstract: This article presents with DYSANOS the first generative market model for smooth SANOS option surfaces for all strikes and expiries which are free of static arbitrage. Our model is designed to generate entire paths of daily spot and option prices for years in the future. We present a robust and useful if somewhat simplistic baseline in the form of an AR(1) model. We discuss model setup, data pipeline, and training and investigate market reconstruction, stability, and tail behavior. We illustrate model performance on 891 Option Metrics IvyDB S\&P Index surfaces from 2022-01-03 through to 2025-08-29. We also demonstrate how to construct numerically a risk-neutral density. As part of this we develop a new test for zero conditional means under a given measure. We show that for 100,000 simulated paths a trading universe of 48 options and spot is numerically free of dynamic arbitrage.