英文标题：
《Option pricing under fast-varying long-memory 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 volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range correlation properties in order to capture such a situation, and we consider European option pricing. This means that the volatility process is neither a Markov process nor a martingale. However, by exploiting the fact that the price process is still a semimartingale and accordingly using the martingale method, we can obtain an analytical expression for the option price in the regime where the volatility process is fast mean-reverting. The volatility process is modeled as a smooth and bounded function of a fractional Ornstein-Uhlenbeck process. We give the expression for the implied volatility, which has a fractional term structure.
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中文摘要：
最近的实证研究表明，在某些市场条件下，基础价格过程的波动性可能具有缓慢衰减的相关性。本文将波动率建模为具有长期相关性的平稳过程，以捕捉这种情况，并考虑了欧式期权定价。这意味着波动过程既不是马尔可夫过程，也不是鞅过程。然而，通过利用价格过程仍然是半鞅的事实，并相应地使用鞅方法，我们可以在波动过程是快速均值回复的情况下获得期权价格的解析表达式。波动过程被建模为分数Ornstein-Uhlenbeck过程的光滑有界函数。我们给出了隐含波动率的表达式，它具有分数期限结构。
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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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