Neural Term Structure of Additive Process for Option Pricing

TL;DR

This paper introduces a neural term structure model for additive processes in option pricing, enabling flexible, data-driven calibration that improves fitting of implied volatility surfaces and simplifies model specification.

Contribution

It proposes using neural networks to model the term structure of additive processes, reducing parametric assumptions and calibration complexity in option pricing models.

Findings

Enhanced flexibility in fitting implied volatility surfaces

Reduced calibration complexity with neural network parameterization

Numerical validation on S&P 500 options demonstrates improved performance

Abstract

The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modeling the underlying log price with an additive process has advantages in easier construction of the risk-neural measure, an explicit option pricing formula and characteristic function, and more flexibility to fit the implied volatility surface. Still, the challenge of calibrating an additive model arises from its time-dependent parameterization, for which one has to prescribe parametric functions for the term structure. For this, we propose the neural term structure model to utilize feedforward neural networks to represent the term structure, which alleviates the difficulty of designing parametric functions and thus attenuates the misspecification risk. Numerical studies with S\&P 500 option data are conducted to evaluate the performance of the neural term structure.