Affine forward variance models

By Jim Gatheral, Martin Keller‐Ressel. Finance and Stochastics, 2018

63 citations recorded by the source corpus.

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 include Hawkes-type models. We show that the cumulant-generating function of an AFI model satisfies a generalised convolution Riccati equation and that a high-frequency limit of AFI models converges in distribution to an AFV model.

Subfields: Computational Mechanics, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/f73789123ad5fbff70957bc9b350efdfc3ab6575

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Eduardo Abi Jaber
2. Sergio Pulido
3. Christa Cuchiero
4. Martin Larsson

In Finance

1. Eduardo Abi Jaber
2. Christa Cuchiero
3. Martin Larsson
4. Sergio Pulido
5. Omar El Euch

In Global and Planetary Change

1. Eduardo Abi Jaber
2. Sergio Pulido
3. Christa Cuchiero
4. Martin Larsson

Citations in the corpus

• A weak solution theory for stochastic Volterra equations of convolution type (2019, methodology): “Alternatively, one can use scaling limits of Hawkes-type processes to generate continuous solutions for well-chosen kernels and affine characteristics (Jaisson and Rosenbaum, 2016; Gatheral and Keller-Ressel, 2019).”