英文标题：
《Option Pricing under Fast-varying and Rough Stochastic Volatility》
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作者：
Josselin Garnier and Knut Solna
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最新提交年份：
2018
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英文摘要：
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the origin. Another classic stylistic feature often assumed for the volatility is that it is mean reverting. In this paper it is shown that the price impact of a rapidly mean reverting rough volatility model coincides with that associated with fast mean reverting Markov stochastic volatility models. This reconciles the empirical observation of rough volatility paths with the good fit of the implied volatility surface to models of fast mean reverting Markov volatilities. Moreover, the result conforms with recent numerical results regarding rough stochastic volatility models. It extends the scope of models for which the asymptotic results of fast mean reverting Markov volatilities are valid. The paper concludes with a general discussion of fractional volatility asymptotics and their interrelation. The regimes discussed there include fast and slow volatility factors with strong or small volatility fluctuations and with the limits not commuting in general. The notion of a characteristic term structure exponent is introduced, this exponent governs the implied volatility term structure in the various asymptotic regimes.
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中文摘要：
最近的实证研究表明，与金融时间序列相关的波动率表现出短期相关性。这意味着波动过程非常粗糙，其自相关在原点处呈现出急剧衰减。波动性的另一个经典风格特征是均值回复。本文表明，快速均值回复粗糙波动率模型的价格影响与快速均值回复马尔可夫随机波动率模型的价格影响一致。这使粗糙波动率路径的经验观察与隐含波动率曲面与快速均值回复马尔可夫波动率模型的良好拟合相一致。此外，该结果与最近关于粗糙随机波动率模型的数值结果一致。它扩展了快速均值回复马尔可夫波动率的渐近结果有效的模型的范围。本文最后对分数波动率渐近及其相互关系进行了一般性讨论。这里讨论的制度包括快速和慢速波动因素，波动性大或小，且限制一般不通勤。引入了特征期限结构指数的概念，该指数控制着各种渐近状态下的隐含波动率期限结构。
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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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