English

From Hawkes-type processes to stochastic volatility

Probability 2018-07-12 v1

Abstract

We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a liquid traded financial instrument in which the nearly unstable regime leads to a Heston-type process where the negative correlation between the noise driving the proce of the instrument and the volatility can be viewed as a result of high variance of the sell-side order arrivals.

Keywords

Cite

@article{arxiv.1807.04192,
  title  = {From Hawkes-type processes to stochastic volatility},
  author = {Łukasz Treszczotko},
  journal= {arXiv preprint arXiv:1807.04192},
  year   = {2018}
}
R2 v1 2026-06-23T02:57:54.630Z