Mathematical Finance· 2026Q1
Convergence of Heavy‐Tailed Hawkes Processes and the Microstructure of Rough Volatility
- 7citations
- Q1SCImago
- 2026year
Short summary
A new method establishes the weak convergence of nearly-unstable Hawkes processes with heavy-tailed kernels, leading to a rough Heston model for financial market price-volatility.
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Key points
- Establishes weak convergence for Hawkes processes with heavy-tailed kernels.
- Derives a scaling limit for a financial market model using these processes.
- The price-volatility process converges to a rough Heston model.
- Introduces a new method for proving tightness of càdlàg processes.
AI-generated from the title and abstract; the full text is not read.
Abstract
ABSTRACT We establish the weak convergence of the intensity of a nearly‐unstable Hawkes process with heavy‐tailed kernel. Our result is used to derive a scaling limit for a financial market model where orders to buy or sell an asset arrive according to a Hawkes process with power‐law kernel. After suitable rescaling the price‐volatility process converges weakly to a rough Heston model. Our convergence result is stronger than previously established ones that have either focused on light‐tailed kernels or the convergence of integrated volatility process. The key is to establish the tightness of the family of rescaled volatility processes. This is achieved by introducing a new method to establish the ‐tightness of càdlàg processes based on the classical Kolmogorov‐Chentsov tightness criterion for continuous processes.
The authors' abstract, as published at the source. Mathematical Finance, 2026 · DOI ↗
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Field: Finance
FinanceEconomics, Econometrics and Finance