This paper presents a novel data-driven approach to option pricing that integrates no-arbitrage theory with machine learning to achieve market resilience. The authors first revisit the homogeneity hint (HH) property, which allows option prices to be expressed as scale-free ratios, but note its limitation: it requires identical risk-neutral return distributions across assets. To overcome this, they introduce a domain shift (DS) approach based on a common representation space. The key idea is to transform asset prices via ρ-scaling, where ρ (volatility scalar) is the root mean square of future volatility. Under this scaling, the risk-neutral distributions of scaled returns become identical, enabling domain adaptation. The authors derive theoretical conditions for this equivalence and provide practical estimation methods for ρ using historical volatility or stochastic volatility models.

Using real data from NIFTY 50 and NIFTY Bank index options, the authors compare HH, DS, and an ensemble model that combines both using a domain shift quotient. The DS model significantly improves prediction accuracy during periods of high market stress (e.g., COVID lockdown), where domain shifts are pronounced. The ensemble model further enhances robustness by dynamically weighting HH and DS components based on the degree of shift. Multi-source training (using data from both indices) shows that the ensemble can reliably price options even for assets with little historical data. The paper emphasizes interpretability by avoiding macroeconomic variables and relying solely on market-derived features. Overall, this work lays a theoretical foundation for domain adaptation in option pricing, demonstrating that data-driven models can be both theoretically grounded and practically effective across diverse market conditions.