Neural Term Structure of Additive Process for Option Pricing

ArXiv ID: 2408.01642 “View on arXiv”

Authors: Unknown

Abstract

The additive process generalizes the Lévy 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.

Keywords: Additive process, Neural term structure, Option pricing, Risk-neutral measure, Implied volatility surface, Equity (Options)

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper is mathematically dense, featuring advanced stochastic calculus, Lévy processes, infinite divisibility, and specific derivations like Lemma 2.1 and Proposition 2.3, placing it at the high end of complexity. It demonstrates strong empirical rigor through calibration with S&P 500 option data, comparison to parametric models, and analysis of robustness across historical surfaces, making it backtest-ready despite focusing on theoretical construction.

  flowchart TD
    A["Research Goal: Assess Neural Term Structure for Additive Process Calibration"] --> B["Data: S&P 500 Options Data"]
    B --> C["Model: Neural Term Structure\nFeedforward Neural Networks"]
    C --> D["Computation: Calibrate Model to Market Data"]
    D --> E["Output: Improved Fit to Implied Volatility Surface"]
    E --> F["Outcome: Reduced Misspecification Risk\nExplicit Pricing Formula Achieved"]