Integrating the implied regularity (Ht) into implied volatility models: A study on free arbitrage model

In financial markets, implied volatility (IV) is a critical metric reflecting the market’s expectations of future price fluctuations in an underlying asset. Research has focused on modeling IV in relation to moneyness. We study the relationship between implied volatility and the implied Hurst exponent H, particularly as they vary with moneyness. Our key finding is that H approaches 1/2 when moneyness is 1, suggesting a critical point in market efficiency expectations at this level. We developed an implied volatility model that integrates H to better capture these dynamics. This model considers the interaction between H and the underlying to strike price ratio S/K, which is crucial for reflecting variations in IV based on moneyness. Applied to many indexes and optimized using the Optuna method, our model, compared with SABR and fSABR, demonstrated promising accuracy, laying the groundwork for future applications in options pricing and volatility forecasting. This approach offers a more nuanced representation of market expectations and the dynamics between IV and H, enhancing both theoretical understanding and practical modeling in financial analysis.