Affine Forward Variance Models

We introduce the class of affine forward variance (AFV) models which includes the Heston model and the rough Heston model. We show that AFV models can be characterized by the affine form of their cumulant generating function... [ view full abstract ]

We introduce the class of affine forward variance (AFV) models which includes the Heston model and the rough Heston model. We show that AFV models can be characterized by the affine form of their cumulant generating function (CGF), which is 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. We show that the AFI model's CGF satisfies a generalized convolution Riccati equation and that a high-frequency limit of AFI models converges to the AFV model.