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

Implied volatility (IV) forecasting is inherently challenging due to its high dimensionality<br>across various moneyness and maturity, and nonlinearity in both spatial and temporal aspects.<br>We utilize implied volatility surfaces (IVS) to represent comprehensive spatial dependence<br>and model the nonlinear temporal dependencies within a series of IVS. Leveraging advanced<br>kernel-based machine learning techniques, we introduce the functional Neural Tangent Kernel<br>(fNTK) estimator within the Nonlinear Functional Autoregression framework, specifically tailored<br>to capture intricate relationships within implied volatilities. We establish the connection<br>between fNTK and kernel regression, emphasizing its role in contemporary nonparametric<br>statistical modeling. Empirically, we analyze S&P 500 Index options from January 2009 to<br>December 2021, encompassing more than 6 million European calls and puts, thereby showcasing<br>the superior forecast accuracy of fNTK.We demonstrate the significant economic value<br>of having an accurate implied volatility forecaster within trading strategies. Notably, short<br>delta-neutral straddle trading, supported by fNTK, achieves a Sharpe ratio ranging from 1.45<br>to 2.02, resulting in a relative enhancement in trading outcomes ranging from 77% to 583%.