Quadratic Hawkes processes for financial prices

@article{Blanc2015QuadraticHP,
  title={Quadratic Hawkes processes for financial prices},
  author={Pierre Blanc and Jonathan Donier and Jean-Philippe Bouchaud},
  journal={Quantitative Finance},
  year={2015},
  volume={17},
  pages={171 - 188}
}
We introduce and establish the main properties of QHawkes (‘Quadratic’ Hawkes) models. QHawkes models generalize the Hawkes price models introduced in Bacry and Muzy [Quant. Finance, 2014, 14(7), 1147–1166], by allowing feedback effects in the jump intensity that are linear and quadratic in past returns. Our model exhibits two main properties that we believe are crucial in the modelling and the understanding of the volatility process: first, the model is time-reversal asymmetric, similar to… 
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