Can a Machine Correct Option Pricing Models?

Abstract

We introduce a novel approach to capture implied volatility smiles. Given any parametric option pricing model used to fit a smile, we train a deep feedforward neural network on the model's orthogonal residuals to correct for potential mispricings and boost performance. Using a large number of recent S&P500 options, we compare our hybrid machine-corrected model to several standalone parametric models ranging from ad-hoc corrections of Black-Scholes to more structural no-arbitrage stochastic volatility models. Empirical results based on out-of-sample fitting errors - in cross-sectional and time-series dimensions - consistently demonstrate that a machine can in fact correct existing models without overfitting. Moreover, we find that our two-step technique is relatively indiscriminate: regardless of the bias or structure of the original parametric model, our boosting approach is able to correct it to approximately the same degree. Hence, our methodology is adaptable and versatile in its application to a large range of parametric option pricing models. As an overarching theme, machine corrected methods, guided by an implied volatility model as a template, outperform pure machine learning methods.