Fast and General Simulation of Lévy-driven OU processes for Energy Derivatives

ArXiv ID: 2401.15483 “View on arXiv”

Authors: Unknown

Abstract

Lévy-driven Ornstein-Uhlenbeck (OU) processes represent an intriguing class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. However, in the current state of play, Monte Carlo simulations of these processes are not straightforward for two main reasons: i) algorithms are available only for some specific processes within this class; ii) they are often computationally expensive. In this paper, we introduce a new simulation technique designed to address both challenges. It relies on the numerical inversion of the characteristic function, offering a general methodology applicable to all Lévy-driven OU processes. Moreover, leveraging FFT, the proposed methodology ensures fast and accurate simulations, providing a solid basis for the widespread adoption of these processes in the energy sector. Lastly, the algorithm allows an optimal control of the numerical error. We apply the technique to the pricing of energy derivatives, comparing the results with the existing benchmarks. Our findings indicate that the proposed methodology is at least one order of magnitude faster than the existing algorithms, while maintaining an equivalent level of accuracy.

Keywords: Lévy-driven Ornstein-Uhlenbeck process, Monte Carlo simulation, characteristic function inversion, energy derivatives pricing, Fast Fourier Transform (FFT), Energy Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper presents advanced mathematical methods involving Lévy processes, characteristic function inversion, and FFT, resulting in a high math complexity score; it also provides a fast simulation algorithm with explicit error control and applies it to energy derivative pricing benchmarks, indicating high empirical readiness.

  flowchart TD
    A["Research Goal: General & Fast Simulation<br>of Lévy-driven OU for Energy"] --> B["Key Methodology: Numerical Inversion<br>of Characteristic Function using FFT"]
    B --> C["Data/Input: Lévy OU Model Parameters<br>(e.g., volatility, jumps, mean reversion)"]
    C --> D["Computational Process:<br>Monte Carlo Simulation"]
    D --> E["Application: Pricing Energy Derivatives"]
    E --> F["Key Finding: 10x Faster Execution<br>vs. Benchmarks"]
    E --> G["Key Finding: Optimal Error Control<br>maintaining Accuracy"]