Paper: arXiv 2603.29430

Authors: Federico M. Bandi, Nicola Fusari, Guido Gazzani, Roberto Renò

Abstract

Options with maturities below one week, hereafter “ultra-short-term” options, have seen a sharp increase in trading activity in recent years. Yet, these instruments are difficult to price jointly using classical pricing models due to the pronounced oscillations observed in the at-the-money implied-volatility term structure across ultra-short-term tenors. We propose Edgeworth++, a parsimonious jump-diffusion model featuring a nonparametric stochastic volatility component, which provides flexibility in capturing implied-volatility smiles for each tenor, combined with a deterministic shift extension, which allows the model to fit rich at-the-money implied-volatility shapes across tenors. We derive a local (in tenor) expansion of the process characteristic function suited to value ultra-short-term options. The expansion leads to fast and accurate option pricing in closed form via standard Fourier inversion. We discuss the benefits of the proposed approach relative to benchmarks.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematically robust extension (Edgeworth++) to classical jump-diffusion models to address complex volatility oscillations in 0DTE and ultra-short-term options. It balances advanced characteristic function expansions with fast Fourier-inversion closed-form pricing suitable for high-frequency volatility surface fitting.

Research Flowchart

  flowchart TD
    A[Research Goal: Jointly price ultra-short-term options < 1 week] --> B[Input: Market option prices with oscillating ATM term structures]
    B --> C[Method: Propose Edgeworth++ Model<br>Jump-diffusion + Nonparametric SV + Deterministic shift]
    C --> D[Derive local expansion of characteristic function in tenor]
    D --> E[Compute option prices via Fourier inversion]
    E --> F[Outcomes: Fast, closed-form pricing fitting rich smiles & ATM term structure]