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

TL;DR

This paper introduces a novel implied volatility model that incorporates the implied Hurst exponent to better capture market dynamics related to moneyness, improving options pricing and volatility forecasting accuracy.

Contribution

The study develops an IV model integrating the implied Hurst exponent H, capturing its interaction with moneyness, and demonstrates its superior performance over existing models like SABR.

Findings

H approaches 1/2 at moneyness 1, indicating market efficiency.

The new model outperforms SABR and fSABR in accuracy.

Enhanced representation of IV-H dynamics improves options pricing.

Abstract

Implied volatility IV is a key metric in financial markets, reflecting market expectations of future price fluctuations. Research has explored IV's relationship with moneyness, focusing on its connection to the implied Hurst exponent H. Our study reveals that H approaches 1/2 when moneyness equals 1, marking a critical point in market efficiency expectations. We developed an IV model that integrates H to capture these dynamics more effectively. This model considers the interaction between H and the underlying-to-strike price ratio S/K, crucial for capturing IV variations based on moneyness. Using Optuna optimization across multiple indexes, the model outperformed SABR and fSABR in accuracy. This approach provides a more detailed representation of market expectations and IV-H dynamics, improving options pricing and volatility forecasting while enhancing theoretical and pratcical financial analysis.