# Hawkes processes for credit indices time series analysis: How random are trades arrival times?

## TL;DR

This paper applies Hawkes processes to model and analyze the timing of trades in credit indices, capturing self-excitement and interactions, and introduces a new fitting method validated on simulated and real data.

## Contribution

It presents a simple, effective maximum likelihood method for fitting multidimensional Hawkes processes with exponential kernels to credit trading data.

## Key findings

- Successfully fitted Hawkes models to real credit index data
- Quantified self-excitement and cross-influence among indices
- Validated the method on simulated data

## Abstract

Targeting a better understanding of credit market dynamics, the authors have studied a stochastic model named the Hawkes process. Describing trades arrival times, this kind of model allows for the capture of self-excitement and mutual interactions phenomena. The authors propose here a simple yet conclusive method for fitting multidimensional Hawkes processes with exponential kernels, based on a maximum likelihood non-convex optimization. The method was successfully tested on simulated data, then used on new publicly available real trading data for three European credit indices, thus enabling quantification of self-excitement as well as volume impacts or cross indices influences.