Paper: arXiv 2406.16400

Authors: Jinniao Qiu, Antony Ware, Yang Yang

Abstract

This paper is devoted to the price-storage dynamics in natural gas markets. A novel stochastic path-dependent volatility model is introduced with path-dependence in both price volatility and storage increments. Model calibrations are conducted for both the price and storage dynamics. Further, we discuss the pricing problem of discrete-time swing options using the dynamic programming principle, and a deep learning-based method is proposed for numerical approximations. A numerical algorithm is provided, followed by a convergence analysis result for the deep-learning approach.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework combining path-dependent rough volatility, commodity storage dynamics, dynamic programming, and deep learning convergence proofs. While the empirical calibration relies on standard optimization techniques, the novelty in price-storage volatility dynamics and deep learning option pricing theory is strong.

Research Flowchart

  flowchart TD
    A[Research Goal: Dynamic Natural Gas Modeling & Swing Option Pricing] --> B[Data Inputs: Historical Price & Storage Data]
    B --> C[Model Calibration: Path-Dependent Volatility in Price & Storage]
    C --> D[Problem Formulation: Swing Option Pricing via Dynamic Programming]
    D --> E[Computational Solver: Deep Learning Numerical Approximation Algorithm]
    E --> F[Outcomes: Validated Model Convergence & Efficient Swing Option Pricing]

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