摘要翻译：
本文研究了Heston模型中远期启动期权和远期隐含波动率微笑在到期日接近零时的渐近性。我们证明了无钱期权的正向微笑爆炸，并计算了一个封闭形式的高阶展开，详细描述了爆炸的速度。此外，结果还表明，方差过程的平方根行为导致了奇异性，使得对于某些参数配置，人们无法获得高阶无钱前向微笑渐近。在货币情况下，一个独立于模型的分析表明，对于任何Ito扩散，小成熟度限制都是很好地定义的。这些证明依赖于急剧大偏差（和精化）的理论，顺便说一句，我们提供了退化大偏差行为的一个例子。
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英文标题：
《The Small-Maturity Heston Forward Smile》
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作者：
Antoine Jacquier and Patrick Roome
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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：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：
  In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the rate of the explosion. Furthermore the result shows that the square-root behaviour of the variance process induces a singularity such that for certain parameter configurations one cannot obtain high-order out-of-the-money forward smile asymptotics. In the at-the-money case a separate model-independent analysis shows that the small-maturity limit is well defined for any Ito diffusion. The proofs rely on the theory of sharp large deviations (and refinements) and incidentally we provide an example of degenerate large deviations behaviour.
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PDF链接：
https://arxiv.org/pdf/1303.4268