Fast Likelihood-Free Parameter Estimation for Lévy Processes
This provides a scalable and practical solution for financial analysts and researchers dealing with complex models like Lévy processes, though it is incremental as it builds on existing simulation-based and neural network frameworks.
The paper tackles the challenge of parameter estimation for Lévy processes in financial modeling, where traditional methods are slow or infeasible due to unavailable likelihoods, by proposing a neural Bayes estimation (NBE) method that outperforms traditional approaches in accuracy and runtime, enabling parameter estimation and uncertainty quantification for a year of high-frequency cryptocurrency data in seconds.
Lévy 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 Lévy 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. We contribute new theoretical results, showing that NBE results in consistent estimators whose risk converges to the Bayes estimator under mild conditions. Moreover, through extensive simulations across several Lévy models, we show that NBE outperforms traditional methods in both accuracy and runtime, while also enabling two complementary approaches to 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.