英文标题：
《Small-time asymptotics for Gaussian self-similar stochastic volatility
  models》
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作者：
Archil Gulisashvili, Frederi Viens, Xin Zhang
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最新提交年份：
2016
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英文摘要：
  We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small-time behaviors of the above depend heavily on the model, and require a control of the asset price density which is uniform with respect to the asset price variable, in order to translate into results for call prices and implied volatilities. Away from the money, we express the asymptotics explicitly using the volatility process\' self-similarity parameter $H$, its first Karhunen-Loeve eigenvalue at time 1, and the latter\'s multiplicity. Several model-free estimators for $H$ result. At the money, a separate study is required: the asymptotics for small time depend instead on the integrated variance\'s moments of orders 1/2 and 3/2, and the estimator for $H$ sees an affine adjustment, while remaining model-free.
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中文摘要：
我们考虑了一类自相似高斯随机波动率模型，并计算了相应资产价格密度、看涨期权定价函数和隐含波动率的小时间（接近到期）渐近性。与著名的极端打击渐近无模型行为不同，上述小时间行为严重依赖于模型，需要控制资产价格密度，该密度与资产价格变量一致，以便转化为买入价格和隐含波动率的结果。除了金钱，我们使用波动过程的自相似参数$H$、其在时间1的第一个Karhunen-Loeve特征值以及后者的多重性显式地表示渐近性。对$H$结果的几个无模型估计。在money，需要进行一项单独的研究：小时间的渐近性取决于1/2阶和3/2阶的综合方差矩，而$H$的估值器看到一个仿射调整，同时保持无模型。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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