英文标题：
《Precise asymptotics: robust stochastic volatility models》
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作者：
Peter K. Friz, Paul Gassiat, Paolo Pigato
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最新提交年份：
2020
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英文摘要：
We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of [Bayer et al; A regularity structure for rough volatility, 2017]. In essence, we implement a Laplace method on the space of models (in the sense of Hairer), which generalizes classical works of Azencott and Ben Arous on path space and then Aida, Inahama--Kawabi on rough path space. When applied to rough volatility models, e.g. in the setting of [Forde-Zhang, Asymptotics for rough stochastic volatility models, 2017], one obtains precise asymptotic for European options which refine known large deviation asymptotics.
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中文摘要：
我们提出了一种新的方法来分析大类（经典和粗糙）随机波动率模型，特别是关于期权价格的短期和小噪声公式。我们的主要工具是规则结构理论，我们以[拜耳等人；粗糙波动率的规则结构，2017年]的形式使用该理论。本质上，我们在模型空间上实现了一种拉普拉斯方法（在海尔意义上），它在路径空间上推广了Azencott和Ben Arous的经典著作，然后在粗糙路径空间上推广了Aida、Inahama和Kawabi的经典著作。当应用于粗糙波动率模型时，例如在【Forde Zhang，粗糙随机波动率模型的渐近性，2017】的设置中，我们可以获得欧洲期权的精确渐近性，这些期权细化了已知的大偏差渐近性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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