Fast and explicit European option pricing under tempered stable processes

ArXiv ID: 2510.01211 “View on arXiv”

Authors: Gaetano Agazzotti, Jean-Philippe Aguilar

Abstract

We provide series expansions for the tempered stable densities and for the price of European-style contracts in the exponential Lévy model driven by the tempered stable process. These formulas recover several popular option pricing models, and become particularly simple in some specific cases such as bilateral Gamma process and one-sided TS process. When compared to traditional Fourier pricing, our method has the advantage of being hyperparameter free. We also provide a detailed numerical analysis and show that our technique is competitive with state-of-the-art pricing methods.

Keywords: Lévy process, tempered stable process, option pricing, series expansions, Fourier pricing, Derivatives

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper presents advanced series expansions and Mellin-Barnes integrals for option pricing under tempered stable processes, requiring deep stochastic calculus and complex analysis. While it includes numerical comparisons and a public GitHub implementation, it lacks rigorous backtesting on real market data or out-of-sample performance metrics.
  flowchart TD
    A["Research Goal: Develop fast & explicit option pricing under<br>Tempered Stable Processes (TSP)"] --> B{"Key Methodology"}
    
    B --> C["Derive Series Expansion for<br>Tempered Stable Density"]
    B --> D["Develop Expansion for European<br>Option Pricing in Exponential Lévy Model"]
    
    C --> E["Computational Process: Series Evaluation"]
    D --> E
    E --> F["Comparison: Hyperparameter-Free Method vs.<br>Traditional Fourier Pricing"]
    
    F --> G{"Key Findings & Outcomes"}
    
    G --> H["Recovers Popular Models (e.g.,<br>Bilateral Gamma, One-sided TS)"]
    G --> I["Competitive Numerical Performance<br>vs. State-of-the-Art Methods"]
    G --> J["Explicit Formulas for<br>Derivatives Pricing"]