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

Chen, Ying and Grith, Maria and Lai, Hannah L. H. (2023): Neural Tangent Kernel in Implied Volatility Forecasting: A Nonlinear Functional Autoregression Approach.

Abstract

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

• Item Type: MPRA Paper
• Language: English
• Keywords: Implied Volatility Surfaces; Neural Networks; Neural Tangent Kernel; Implied Volatility Forecasting; Nonlinear Functional Autoregression; Option Trading Strategies
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C45 - Neural Networks and Related Topics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation

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