Fast Likelihood-Free Parameter Estimation for L'evy Processes

2025-05-03

AI Summary

提出基于神经贝叶斯估计(NBE)的快速无似然方法，解决Lévy过程参数估计难题，通过仿真与神经网络实现高效准确的参数推断与不确定性量化。

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Probabilistic InferenceIntelligent Robots: State Estimation

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsUser Modeling, Personalization and Recommendation: Practical large-scale studies of user experienceWeb Mining and Content Analysis: Models for Web evolution

Abstract

L'evy processes are widely used in financial modeling due to their ability to capture discontinuities and heavy tails, which are common in high-frequency asset return data. However, parameter estimation remains a challenge when associated likelihoods are unavailable or costly to compute. We propose a fast and accurate method for L'evy parameter estimation using the neural Bayes estimation (NBE) framework -- a simulation-based, likelihood-free approach that leverages permutation-invariant neural networks to approximate Bayes estimators. Through extensive simulations across several L'evy models, we show that NBE outperforms traditional methods in both accuracy and runtime, while also enabling rapid bootstrap-based uncertainty quantification. We illustrate our approach on a challenging high-frequency cryptocurrency return dataset, where the method captures evolving parameter dynamics and delivers reliable and interpretable inference at a fraction of the computational cost of traditional methods. NBE provides a scalable and practical solution for inference in complex financial models, enabling parameter estimation and uncertainty quantification over an entire year of data in just seconds. We additionally investigate nearly a decade of high-frequency Bitcoin returns, requiring less than one minute to estimate parameters under the proposed approach.

Problem

• Estimating parameters for Lévy processes without likelihoods
• Improving accuracy and speed in financial model inference
• Enabling rapid uncertainty quantification in high-frequency data

Innovation

• Neural Bayes estimation for Levy processes
• Simulation-based likelihood-free parameter estimation
• Permutation-invariant neural networks approximation