英文标题：
《Affine forward variance models》
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作者：
Jim Gatheral and Martin Keller-Ressel
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最新提交年份：
2018
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英文摘要：
  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.
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中文摘要：
我们介绍了一类仿射前向方差（AFV）模型，其中常规Heston模型和粗糙Heston模型都是这类模型的特例。我们证明，AFV模型可以用其累积量母函数的仿射形式来表征，其可以作为卷积Riccati方程的解来获得。我们进一步介绍了一类仿射前序流强度（AFI）模型，其结构类似于AFV模型，但由跳跃过程驱动，包括Hawkes型模型。我们证明了AFI模型的累积量母函数满足广义卷积Riccati方程，并且AFI模型的高频极限在分布上收敛于AFV模型。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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