Affine forward variance models
Affine forward variance models
复制标题
DOI：
10.1007/s00780-019-00392-5
复制
发表时间：
2019-07-01
影响因子：
1.7
通讯作者：
Keller-Ressel, Martin
中科院分区：
文献类型：
--
作者：
Gatheral, Jim;Keller-Ressel, Martin
本文介绍了一类仿射前向方差（AFV）模型，传统的赫斯顿模型和粗糙的赫斯顿模型都是这类模型的特例。我们表明，AFV模型可以通过其累积生成函数的仿射形式来表征，该函数可以作为卷积Riccati方程的解来获得。我们进一步介绍类仿射前向阶流强度（AFI）模型，这是结构上类似于AFV模型，但由跳跃过程驱动，其中包括霍克斯型模型。我们表明，累积生成函数的AFI模型满足广义卷积Riccati方程和AFI模型的高频限制收敛分布的AFV模型。
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.