Neural Tangent Kernel in Implied Volatility Forecasting: A Nonlinear Functional Autoregression Approach

Abstract: Implied volatility (IV) remains a pivotal yet intricate component of financial markets, posing continuous challenges for accurate forecasting. We present a Nonlinear Functional Autoregression framework tailored to the series of implied volatility surfaces-a dynamic domain influenced by moneyness and maturity. This approach, designed for European put and call options, adeptly navigates the nonlinear and asymmetric temporal and spatial dependencies intrinsic to IV. Central to our approach is the functional Neural Tangent Kernel (fNTK) estimator. Grounded in the Neural Tangent Kernel parameterization, this estimator presents a modern statistical solution, parsing the intertwined dependencies found within the projections on the covariance operator of the IV surfaces’ time series. A methodological contribution lies in establishing the nexus between fNTK and kernel regression, emphasizing fNTK’s place in contemporary nonparametric statistical modeling. Transitioning from methodology to empirical evidence, we showcase the framework’s real-world utility via an analysis of the S&P 500 index spanning January 2009 to December 2021. The fNTK not only stands out in forecasting accuracy, achieving an average improvement of 4.54% to 39.44% in RMSE forecast accuracy for 5 to 20-day-ahead forecasts but also paves the way for practical trading strategies. When underpinned by our model, straddle trading yields a remarkable Sharpe ratio between 3.72 and 5.41, culminating in a staggering 107.79% to 528.36% relative enhancement in trading results. This convergence of methodological rigor and empirical results offers both a statistical advancement and a beacon for practitioners in the options market. Joint paper with Maria Grith and Hannah Lai.

Link to paper.