摘要翻译：
利用Figueroa-Lopez&Houdre(2009)中给出的分布函数的小时间展开式，结合Esscher变换的num\'eraire的变化，导出了指数Levy模型下的货币外看涨期权的小时间展开式。特别地，我们量化地发现驱动L\'e}vy过程的高斯分量的非零波动率$\\sigma$的影响是将呼叫价格增加$1/2\sigma^2t^2e^{k}\nu(k)(1+O(1))$as$t\到0$，其中$\nu$是L\'evy密度。利用看涨期权的小时间展开式，我们得到了隐含波动率的小时间展开式，它使Tankov(2010)给出的一阶估计变得尖锐。数值结果表明，二阶近似比一阶近似有更好的性能。我们的结果也推广到一类时变L\'evy模型。我们还考虑了CGMY模型的一个小时间、小对数货币机制，并将此方法应用于到位价看涨期权的小时间定价。
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英文标题：
《The small-maturity smile for exponential Levy models》
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作者：
Jose E. Figueroa-Lopez and Martin Forde
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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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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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英文摘要：
  We derive a small-time expansion for out-of-the-money call options under an exponential Levy model, using the small-time expansion for the distribution function given in Figueroa-Lopez & Houdre (2009), combined with a change of num\'eraire via the Esscher transform. In particular, we quantify find that the effect of a non-zero volatility $\sigma$ of the Gaussian component of the driving L\'{e}vy process is to increase the call price by $1/2\sigma^2 t^2 e^{k}\nu(k)(1+o(1))$ as $t \to 0$, where $\nu$ is the L\'evy density. Using the small-time expansion for call options, we then derive a small-time expansion for the implied volatility, which sharpens the first order estimate given in Tankov (2010). Our numerical results show that the second order approximation can significantly outperform the first order approximation. Our results are also extended to a class of time-changed L\'evy models. We also consider a small-time, small log-moneyness regime for the CGMY model, and apply this approach to the small-time pricing of at-the-money call options.
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PDF链接：
https://arxiv.org/pdf/1105.3180