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arXiv · 1807.04192

From Hawkes-type processes to stochastic volatility

Łukasz Treszczotko
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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.

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Łukasz Treszczotko. 2018-07-11. From Hawkes-type processes to stochastic volatility. https://arxiv.org/abs/1807.04192

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