论文标题
局部粗糙的路径空间，以进行粗糙的波动
A partial rough path space for rough volatility
论文作者
论文摘要
我们开发了一种粗糙路径理论的变体，用于分析一类称为粗糙波动率模型的金融资产价格模型。作为一种应用，我们证明了某种类别的粗糙波动率模型的路径大偏差原理（LDP），进而描述了这些模型下的隐含波动性的限制行为。首先，我们在其上引入了部分粗糙的路径空间和一个集成图，然后研究了几个基本属性，包括集成图的本地Lipschitz连续性，从部分粗糙的路径空间到粗糙的路径空间。其次，我们构建了粗糙波动率模型的粗糙路径提升。最后，我们在部分粗糙路径空间上证明了一家不民党，而粗糙挥发性的LDP随后是由粗糙微分方程的解决方案映射的连续性。
We develop a variant of rough path theory tailor-made for analyzing a class of financial asset price models known as rough volatility models. As an application, we prove a pathwise large deviation principle (LDP) for a certain class of rough volatility models, which in turn describes the limiting behavior of implied volatility for short maturity under those models. First, we introduce a partial rough path space and an integration map on it and then investigate several fundamental properties including local Lipschitz continuity of the integration map from the partial rough path space to a rough path space. Second, we construct a rough path lift of a rough volatility model. Finally, we prove an LDP on the partial rough path space, and the LDP for rough volatility then follows by the continuity of the solution map of rough differential equations.
