英文标题：
《To sigmoid-based functional description of the volatility smile》
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作者：
Andrey Itkin
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最新提交年份：
2014
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英文摘要：
We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied volatilities which demonstrate smile or skew. An arbitrage-free calibration algorithm is considered that constructs the implied volatility surface as a grid in the strike-expiration space and guarantees a lack of arbitrage at every node of this grid. We also demonstrate how to construct an arbitrage-free interpolation and extrapolation in time, as well as build a local volatility and implied pdf surfaces. Asymptotic behavior of this parameterization is discussed, as well as results on stability of the calibrated parameters are presented. Numerical examples show robustness of the proposed approach in building all these surfaces as well as demonstrate a better quality of the fit as compared with some known models.
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中文摘要：
我们提出了一种新的隐含波动率曲面的静态参数化方法，该方法是利用sigmoid函数的多项式结合其他项构造的。这种参数化非常灵活，足以适应市场隐含的波动，这些波动表现出微笑或扭曲。考虑了一种无套利校准算法，该算法将隐含波动率曲面构造为罢工到期空间中的网格，并保证该网格的每个节点都不存在套利。我们还演示了如何在时间上构造无套利插值和外推，以及如何构建局部波动率和隐含pdf曲面。讨论了这种参数化的渐近行为，给出了标定参数稳定性的结果。数值算例表明，与一些已知模型相比，所提出的方法在构建所有这些曲面时具有鲁棒性，并且显示出更好的拟合质量。
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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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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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一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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