Affine forward variance models

@article{Gatheral2019AffineFV,
  title={Affine forward variance models},
  author={Jim Gatheral and Martin Keller-Ressel},
  journal={Finance and Stochastics},
  year={2019},
  volume={23},
  pages={501-533}
}
We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterised by the affine form of their cumulant-generating function, which can be obtained as solution of a convolution Riccati equation. We further introduce the class of affine forward order flow intensity (AFI) models, which are structurally similar to AFV models, but driven by jump processes, and which… 

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