Affine Forward Variance Models
Finance and Stochastics, Forthcoming
30 Pages Posted: 28 Jan 2018 Last revised: 12 Jun 2019
Date Written: January 19, 2018
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 characterized 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 include Hawkes-type models. We show that the cumulant generating function of an AFI model satisfies a generalized convolution Riccati equation and that a high-frequency limit of AFI models converges in distribution to the AFV model.
Keywords: Rough Volatility, Affine Process, Stochastic Volatility, Hawkes Process, Forward Variance
JEL Classification: G13, C02
Suggested Citation: Suggested Citation