英文标题：
《Filling the gaps smoothly》
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作者：
Andrey Itkin, Alexander Lipton
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最新提交年份：
2016
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英文摘要：
The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the approach proposed in LiptonSepp2011 is developed by i) replacing a piecewise constant local variance construction with a piecewise linear one, and ii) allowing non-zero interest rates and dividend yields. Our approach remains analytically tractable; it combines the Laplace transform in time with an analytical solution of the resulting spatial equations in terms of Kummer\'s degenerate hypergeometric functions.
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中文摘要：
将局部波动率模型校准到给定的期权价格集是数学金融学的一个经典问题。多篇论文都考虑了这一点，并提出了各种解决方案。本文对LiptonSepp2011中提出的方法进行了扩展，即i）用分段线性结构替换分段常数局部方差结构，以及ii）允许非零利率和股息收益率。我们的方法在分析上仍然可行；它将拉普拉斯时间变换与根据Kummer退化超几何函数得到的空间方程的解析解相结合。
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分类信息：

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：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：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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