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

Fuente: arXiv
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Autori principali: Baviera, Roberto, Manzoni, Pietro
Natura: Preprint
Pubblicazione: 2024
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author Baviera, Roberto
Manzoni, Pietro
author_facet Baviera, Roberto
Manzoni, Pietro
contents 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 explicit 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_15483
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Fast and General Simulation of Lévy-driven Ornstein Uhlenbeck processes for Energy Derivatives
Baviera, Roberto
Manzoni, Pietro
Computational Finance
Mathematical Finance
Pricing of Securities
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 explicit 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.
title Fast and General Simulation of Lévy-driven Ornstein Uhlenbeck processes for Energy Derivatives
topic Computational Finance
Mathematical Finance
Pricing of Securities
url https://arxiv.org/abs/2401.15483