# Multi-kernel property in high-frequency price dynamics under Hawkes model

## TL;DR

This paper introduces a multi-kernel Hawkes model to capture different responsive speeds of market participants in high-frequency trading, validated with empirical US stock data.

## Contribution

It proposes a novel multi-kernel Hawkes framework for modeling high-frequency price dynamics and assesses the optimizer's effectiveness in complex likelihood landscapes.

## Key findings

- Identification of UHF, VHF, and HF kernels in US stock data
- Estimation of arrival times and contribution levels for each kernel
- Validation of the model's ability to capture diverse market participant behaviors

## Abstract

This study investigates and uses multi-kernel Hawkes models to describe a high-frequency mid-price process. Each kernel represents a different responsive speed of market participants. Using the conditional Hessian, we examine whether the numerical optimizer effectively finds the global maximum of the log-likelihood function under complicated modeling. Empirical studies that use stock prices in the US equity market show the existence of multi-kernels classified as ultra-high-frequency (UHF), very-high-frequency (VHF), and high-frequency (HF). We estimate the conditional expectations of arrival times and the degree of contribution to the high-frequency activities for each kernel.