摘要翻译：
设$\sigma_t(x)$表示到期日的隐含波动率$t$，对于一个罢工$k=s_0e^{xt}$，其中$x\in\bbr$和$s_0$是标的的当前值。在仿射随机波动率模型类中，当成熟度$T$趋于无穷大时，$\sigma_t(x)$具有一致的极限，公式为$\sigma_\infty(x)=\sqrt{2}(H^*(x)^{1/2}+(H^*(x)-x)^{1/2})$。函数$h^*$是标度对数点过程的极限累积量母函数$h$的凸对偶。我们用底层模型的功能特性来表示$h$。极限公式的证明依赖于标度对数点过程在时间趋于无穷大时的大偏差行为。我们将我们的结果应用于几类应用中的带跳跃的随机波动模型（如状态无关跳跃的Heston模型、状态相关跳跃的Bates模型和Barndorff-Nielsen-Shephard模型）的极限微笑。
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英文标题：
《Large deviations and stochastic volatility with jumps: asymptotic
  implied volatility for affine models》
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作者：
Antoine Jacquier, Martin Keller-Ressel and Aleksandar Mijatovic
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最新提交年份：
2011
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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：
  Let $\sigma_t(x)$ denote the implied volatility at maturity $t$ for a strike $K=S_0 e^{xt}$, where $x\in\bbR$ and $S_0$ is the current value of the underlying. We show that $\sigma_t(x)$ has a uniform (in $x$) limit as maturity $t$ tends to infinity, given by the formula $\sigma_\infty(x)=\sqrt{2}(h^*(x)^{1/2}+(h^*(x)-x)^{1/2})$, for $x$ in some compact neighbourhood of zero in the class of affine stochastic volatility models. The function $h^*$ is the convex dual of the limiting cumulant generating function $h$ of the scaled log-spot process. We express $h$ in terms of the functional characteristics of the underlying model. The proof of the limiting formula rests on the large deviation behaviour of the scaled log-spot process as time tends to infinity. We apply our results to obtain the limiting smile for several classes of stochastic volatility models with jumps used in applications (e.g. Heston with state-independent jumps, Bates with state-dependent jumps and Barndorff-Nielsen-Shephard model).
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PDF链接：
https://arxiv.org/pdf/1108.3998