Implied volatility is (almost) past-dependent: Linear vs non-linear models

We explore and demonstrate a clear pattern of past-dependence in predicting implied volatility, which extends up to twenty days and is present in both linear and nonlinear models. Empirically, we find that linear models utilizing precedent values up to 20 days explain up to 80% of the variance in the S&P 500 index, while nonlinear models explain 78%. Furthermore, we observe that L2 regularization, as opposed to L1, enhances the performance of linear models and underscores the importance of past-dependence. As a result, a simple linear model with L2 regularization, incorporating precedent values up to the past 20 days, consistently outperforms both linear and nonlinear benchmark models when applied to the S&P 500 index option and SSE 50 ETF option over the past decades. Additionally, we uncover that the impact of all preceding values exists but consistently diminishes over time in all empirical studies involving past-dependence settings. Finally, we demonstrate that these forecasts yield profitable outcomes when implementing a simple long-short portfolio trading strategy. This study primarily investigates the ‘path-dependency’ of implied volatility in financial markets and further confirms that simple models can sometimes surpass complex nonlinear models in predicting volatility.