GROMM: A No-Arbitrage Generative Risk-Neutral Option Market Model Based on the SANOS Framework

The study proposes GROMM, a static and dynamic no-arbitrage European option market model based on the SANOS framework, which enables smooth interpolation between option prices, and has proven that its dynamics have a unique strong solution. The model is validated on S&P index option data from January 2022 to August 2025, with initial states fitting over 95% of relevant market option prices within the bid-ask spread. The model maintains no-arbitrage properties after training under both P and Q measures while fitting market dynamics well, and the study also proposes a series of BHW tests for checking no-arbitrage.