Convergence of Heavy-Tailed Hawkes Processes and the Microstructure of Rough Volatility

Ulrich Horst, Wei Xu and Rouyi Zhang

Papers from arXiv.org

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 much 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 methods to establish the $C$-tightness of c\`adl\`ag processes based on the classical Kolmogorov-Chentsov tightness criterion for continuous processes.

Date: 2023-12, Revised 2024-11
New Economics Papers: this item is included in nep-mst and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2312.08784

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