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.
Cite
@article{arxiv.1807.04192,
title = {From Hawkes-type processes to stochastic volatility},
author = {Łukasz Treszczotko},
journal= {arXiv preprint arXiv:1807.04192},
year = {2018}
}