2023/12/14 by Ulrich Horst, Wei Xu, Horst, Ulrich +3
Mathematics · #60F05 #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Point processes and geometric inequalities #Primary 60G55 #Probability (math.PR) #secondary 60G22
paper · pdf · doi:10.48550/arxiv.2312.08784
openalex publication_date 2023/12/14 · openalex created_date 2023/12/16 · openalex updated_date 2026/07/28
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 methods to establish the C-tightness of càdlàg processes based on the classical Kolmogorov-Chentsov tightness criterion for continuous processes.