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摘要翻译：
本文研究了在成熟度较小，但与随机波动因子的均值回复时间相比较大的情况下的随机波动模型。该问题属于非线性HJB型方程的平均/均匀化问题，其中“快变量”位于非紧空间。我们发展了一个基于粘度解的一般性论点，并将其应用于本文所研究的两个体系。我们导出了一个大偏差原理，并推导了货币外看涨期权和看跌期权的渐近价格及其相应的隐含挥发度。本文的结果推广了Feng,Forde和Fouque[SIAM J.Financial Math.1(2010)126-141]中关于Heston模型的矩母函数计算的结果。
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英文标题：
《Small-time asymptotics for fast mean-reverting stochastic volatility
models》
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作者：
Jin Feng, Jean-Pierre Fouque, Rohini Kumar
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最新提交年份：
2012
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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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英文摘要：
In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB-type equations where the "fast variable" lives in a noncompact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle, and we deduce asymptotic prices for out-of-the-money call and put options, and their corresponding implied volatilities. The results of this paper generalize the ones obtained in Feng, Forde and Fouque [SIAM J. Financial Math. 1 (2010) 126-141] by a moment generating function computation in the particular case of the Heston model.
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PDF链接：
https://arxiv.org/pdf/1009.2782
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