Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness

虚假平稳粗糙Heston波动率：微结构启发的基础

Fake stationary rough Heston volatility: Microstructure-inspired foundations

本文提出了一种基于时间非齐性粗糙分数CIR方程的虚假平稳粗糙Heston波动率模型，研究其在重尾核函数下的渐进行为及性质。

双变量近不稳定霍克斯过程的尺度极限及其在粗糙波动率中的应用

Scaling Limits of Bivariate Nearly-Unstable Hawkes Processes and Applications to Rough Volatility

研究通过单向交叉激励耦合的一对近不稳定霍克斯过程，证明其强度向量弱收敛到粗糙波动率型随机Volterra方程组的唯一解，并得到短时交叉去相关律。

局部随机波动率模型的粗糙偏微分方程

Rough PDEs for local stochastic volatility models

本研究提出一种适用于非马尔可夫局部随机波动率模型的新型定价方法，通过粗糙路径理论结合Feynman-Kac型公式建立粗糙偏微分方程定价框架，对波动率形式依赖极小，可广泛应用于经典及粗糙LSV模型的欧式期权定价。

Hybrid simulation scheme for volatility modulated moving average fields

We develop a simulation scheme for a class of spatial stochastic processes called volatility modulated moving averages. A characteristic feature of this model is that the behaviour of the moving average kernel at zero governs the roughness of realisations, whereas its behaviour away from zero determines the global properties of the process, such as long range dependence. Our simulation scheme takes this into account and approximates the moving average kernel by a power function around zero and by a step function elsewhere. For this type of approach the authors of [8], who considered an analogo…

The characteristic function of Gaussian stochastic volatility models: an analytic expression

Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample paths. This is made possible by virtue of the flexibility introduced in the choice of the covariance function of the Gaussian process. The price to pay is that, in general, such models are no longer Markovian nor semimartingales, which limits their practical use. We derive, in two different ways, an explicit analytic expression for the joint characteristic funct…

本地化波动

Localizing Volatilities

我们提出了Gyöngy（1986）的非齐次马尔可夫随机微分方程的构造的两个主要应用，该方程模拟了连续伊藤过程的一维边缘。首先证明了Dupire（1994）和Derman和Kani（1994）的结果。然后，我们提出了贝塞尔为基础的随机波动率模型，在这种关系是用来计算本地波动率的解析公式。其次，我们使用这些模仿技术，以扩展著名的本地波动率的结果，随机利率框架。

订单流、市场影响和波动的统一理论

A unified theory of order flow, market impact, and volatility

本文提出了一种统一模型，通过Hawkes过程区分核心订单与反应流，揭示订单流、波动性和市场影响之间的内在联系。

当摩擦是分数阶的：高频数据中的粗糙噪声

When Frictions are Fractional: Rough Noise in High-Frequency Data

本文针对高频金融数据中的粗糙市场微观结构噪声，提出基于连续伊藤半鞅的估计方法，推导噪声粗糙度参数及积分波动率的一致估计量和置信区间，并解释波动率特征图的发散现象。

Captive Jump Processes

We explicitly construct so-called captive jump processes. These are stochastic processes in continuous time, whose dynamics are confined by a time-inhomogeneous bounded domain. The drift and volatility of the captive processes depend on the domain's boundaries which in turn restricts the state space of the process. We show how an insurmountable shell may contain the captive jump process while the process may jump within the restricted domain. In a further development, we also show how - within a confined domain - inner time-dependent corridors can be introduced, which a captive jump process ma…