摘要翻译：
在无限变差CGMY L{e}vy模型下，导出了接近货币的欧式期权价格的三阶近似，并将其推广到具有独立布朗分量的模型。考虑的渐近机制，即当到期日接近零时，使罢工收敛到现货股票价格，在应用中是相关的，因为最具流动性的期权有接近现货价格的罢工。我们的结果揭示了连续分量和跳跃参数的波动性与临近到期时期权价格行为之间的联系，当罢工接近现货价格时。特别地，发现了一种新的跃迁现象，其中三阶项表现出两种不同的渐近状态，这两种状态取决于$y\In(1,3/2)$或$y\In(3/2,2)$。与二阶近似不同，这里的展开式是非常精确的，因此它们实际上可以用来校准一些模型参数。为了说明，我们将Brownian分量的波动率$\sigma$和CGMY模型的跳跃强度$C$校准到实际期权价格。
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英文标题：
《Third-Order Short-Time Expansions for Close-to-the-Money Option Prices
  under the CGMY Model》
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作者：
Jos\'e E. Figueroa-L\'opez, Ruoting Gong, Christian Houdr\'e
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最新提交年份：
2017
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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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英文摘要：
  A third-order approximation for close-to-the-money European option prices under an infinite-variation CGMY L\'{e}vy model is derived, and is then extended to a model with an additional independent Brownian component. The asymptotic regime considered, in which the strike is made to converge to the spot stock price as the maturity approaches zero, is relevant in applications since the most liquid options have strikes that are close to the spot price. Our results shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of option prices near expiration when the strike is close to the spot price. In particular, a new type of transition phenomenon is uncovered in which the third order term exhibits two distinct asymptotic regimes depending on whether $Y\in(1,3/2)$ or $Y\in(3/2,2)$. Unlike second order approximations, the expansions herein are shown to be remarkably accurate so that they can actually be used for calibrating some model parameters. For illustration, we calibrate the volatility $\sigma$ of the Brownian component and the jump intensity $C$ of the CGMY model to actual option prices.
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PDF链接：
https://arxiv.org/pdf/1305.4719