5 papers
Convergence of Heavy-Tailed Hawkes Processes and the Microstructure of Rough Volatility
Ulrich Horst, Wei Xu, Rouyi Zhang
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…
Microstructural Foundation of Rough Log-Normal Volatility Models
Paul P. Hager, Ulrich Horst, Thomas Wagenhofer +1
We establish a microstructural foundation of the rough Bergomi model. Specifically, we consider a sequence of order driven financial market models where orders to buy or sell an as…
Second-Order Regular Variation and Second-Order Approximation of Hawkes Processes
Ulrich Horst, Wei Xu
This paper provides and extends second-order versions of several fundamental theorems on first-order regularly varying functions such as Karamata's theorem/representation and Taube…
Functional Limit Theorems for Hawkes Processes
Ulrich Horst, Wei Xu
We prove that the long-run behavior of Hawkes processes is fully determined by the average number and the dispersion of child events. For subcritical processes we provide FLLNs and…
Path-dependent Fractional Volterra Equations and the Microstructure of Rough Volatility Models driven by Poisson Random Measures
Ulrich Horst, Wei Xu, Rouyi Zhang
We consider a microstructure foundation for rough volatility models driven by Poisson random measures. In our model the volatility is driven by self-exciting arrivals of market ord…