A Hawkes model with CARMA(p,q) intensity
In this paper we introduce a new model named CARMA(p,q)-Hawkes process as the Hawkes model with exponential kernel implies a strictly decreasing behaviour of the autocorrelation function and empirically evidences reject the monotonicity assumption on the autocorrelation function. The proposed model is a Hawkes process where the intensity follows a Continuous Time Autoregressive Moving Average (CARMA) process and specifically is able to reproduce more realistic dependence structures. We also study the conditions of stationarity and positivity for the intensity and the strong mixing property for the increments. Furthermore we compute the likelihood, present a simulation method and discuss an estimation method based on the autocorrelation function. A simulation and estimation exercise highlights the main features of the CARMA(p,q)-Hawkes.
Code (0)
등록된 구현이 없습니다.
Tasks
modelSimilar Papers 제목 키워드 기반
Option Pricing with a Compound CARMA(p,q)-Hawkes
A self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p,q)-Hawkes model, has recently been introduced. The model generalizes the Hawkes process by substituting …
Variance-Hawkes Process and its Application to Energy Markets
We define a new model using a Hawkes process as a subordinator in a standard Brownian motion. We demonstrate that this Hawkes subordinated Brownian motion or more succinctly, variance-Hawkes process can be fit to 2018 an…
On Hawkes Processes with Infinite Mean Intensity
The stability condition for Hawkes processes and their non-linear extensions usually relies on the condition that the mean intensity is a finite constant. It follows that the total endogeneity ratio needs to be strictly …
UnityPricing VIX options under the Heston-Hawkes stochastic volatility model
We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clusteri…
Non-Parametric Estimation of Multi-dimensional Marked Hawkes Processes
An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. Whil…