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摘要翻译：
在过去的十年里，人们对与一般的看涨定价函数相关的隐含波动率的渐近行为进行了广泛的研究。本文主要讨论了隐含波动率的Lee矩公式和Piterbarg猜想，该猜想描述了股票价格的所有矩都是有限的情况下隐含波动率的行为。我们在李氏矩公式中找到了保证极限存在的各种条件。我们还证明了Piterbarg猜想的一个改进版本，并给出了该猜想在其原始形式下的有效性的一个非限制性充分条件。本文所得到的渐近公式分别应用于具有双指数跳跃律的复合泊松过程扰动的CEV模型和Heston模型中的隐含波动率。
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英文标题：
《Asymptotic equivalence in Lee's moment formulas for the implied
volatility and Piterbarg's conjecture》
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作者：
Archil Gulisashvili
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最新提交年份：
2010
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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：
The asymptotic behavior of the implied volatility associated with a general call pricing function has been extensively studied in the last decade. The main topics discussed in this paper are Lee's moment formulas for the implied volatility, and Piterbarg's conjecture, describing how the implied volatility behaves in the case where all the moments of the stock price are finite. We find various conditions guaranteeing the existence of the limit in Lee's moment formulas. We also prove a modified version of Piterbarg's conjecture and provide a non-restrictive sufficient condition for the validity of this conjecture in its original form. The asymptotic formulas obtained in the paper are applied to the implied volatility in the CEV model and in the Heston model perturbed by a compound Poisson process with double exponential law for jump sizes.
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PDF链接：
https://arxiv.org/pdf/1007.5353
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