摘要翻译：
我们考虑一类资产，其风险中性定价动力学由一个指数L\'Evy型过程描述，并以违约为约束。这类过程的特征包括局部相关的漂移、扩散和缺省强度，以及局部相关的L\'evy测度。利用正则摄动理论和傅立叶分析的方法，我们得到了欧式期权价格的级数展开式。我们还提供了该级数展开收敛到精确价格的精确条件。另外，对于模型框架中的某一子类资产，我们导出了由期权定价公式引起的隐含波动率的扩展。隐含波动率扩张在收敛半径内是精确的。作为我们框架的一个例子，我们提出了一类类CEV的L\'evy型模型。在这一类中，近似的期权价格可以通过一个傅立叶积分来计算，近似的隐含挥发是显式的（即不需要积分）。此外，类CEV的L\'Evy型模型可以很好地拟合S{&}P500指数期权的隐含波动率面。
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英文标题：
《The Smile of certain L\'evy-type Models》
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作者：
Antoine Jacquier, Matthew Lorig
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最新提交年份：
2013
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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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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英文摘要：
  We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity as well as a locally-dependent L\'evy measure. Using techniques from regular perturbation theory and Fourier analysis, we derive a series expansion for the price of a European-style option. We also provide precise conditions under which this series expansion converges to the exact price. Additionally, for a certain subclass of assets in our modeling framework, we derive an expansion for the implied volatility induced by our option pricing formula. The implied volatility expansion is exact within its radius of convergence. As an example of our framework, we propose a class of CEV-like L\'evy-type models. Within this class, approximate option prices can be computed by a single Fourier integral and approximate implied volatilities are explicit (i.e., no integration is required). Furthermore, the class of CEV-like L\'evy-type models is shown to provide a tight fit to the implied volatility surface of S{&}P500 index options.
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PDF链接：
https://arxiv.org/pdf/1207.1630