From Volatility to Variance: A Skew-Enhanced SABR Model and Its Empirical Study in the Chinese Financial Options Market

Accurately characterizing the implied volatility curves is a central challenge in option pricing and risk management. The classical SABR model by Hagan et al. has been widely adopted in practice due to its well-defined stochastic volatility structure and its tractable closed-form approximation for Black implied volatility. However, under complex market conditions, its fitting accuracy for implied volatility curves remains limited. To address this issue, this paper proposes an extended model within the SABR framework, referred to as skew-SABR. Specifically, the proposed approach introduces an extension to the stochastic dynamics of the underlying asset price and its variance process, under which a corresponding Black implied volatility expression is derived. By further simplifying and reorganizing the resulting formula, the implied volatility can be expressed in a form that explicitly incorporates a skew parameter, thereby enabling a direct characterization of the asymmetry in the implied volatility curve. The resulting expression preserves the structural simplicity of the Hagan-SABR formula, while significantly enhancing the model's flexibility in capturing complex volatility smile patterns. From a theoretical perspective, the paper provides a systematic analysis of the model specification and the financial interpretation of its parameters. From an empirical perspective, a comprehensive comparison is conducted using data from the Chinese options market over the period 2018--2025. The skew-SABR model is evaluated against the classical Hagan-SABR model, the SVI parameterization, polynomial fitting, and spline-based methods. Numerical results show that, across different market regimes and a wide range of implied volatility curve shapes, the skew-SABR model consistently achieves high and stable fitting accuracy.