# Marked Hawkes process modeling of price dynamics and volatility estimation

## TL;DR

This paper extends Hawkes process models to include marks for more realistic equity price tick modeling, analyzing jumps, dependencies, and deriving volatility estimates validated through simulations and empirical data.

## Contribution

The paper introduces a marked Hawkes process model for equity prices, incorporating jumps and dependencies, and derives a new volatility formula validated against real data.

## Key findings

- Marked Hawkes model effectively captures price jump dynamics.
- Derived volatility formula aligns with realized volatility in studies.
- Model improves understanding of intraday volatility estimation.

## Abstract

A simple Hawkes model have been developed for the price tick structure dynamics incorporating market microstructure noise and trade clustering. In this paper, the model is extended with random mark to deal with more realistic price tick structures of equities. We examine the impact of jump in price dynamics to the future movements and dependency between the jump sizes and ground intensities. We also derive the volatility formula based on stochastic and statistical methods and compare with realized volatility in simulation and empirical studies. The marked Hawkes model is useful to estimate the intraday volatility similarly in the case of simple Hawkes model.