英文标题：
《Uncertain Volatility Models with Stochastic Bounds》
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作者：
Jean-Pierre Fouque and Ning Ning
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最新提交年份：
2017
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英文摘要：
  In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead of using two deterministic bounds, the uncertain volatility fluctuates between two stochastic bounds generated by its inherent stochastic volatility process. This brings better accuracy and is consistent with the observed volatility path such as for the VIX as a proxy for instance. We apply the regular perturbation analysis upon the worst case scenario price, and derive the first order approximation in the regime of slowly varying stochastic bounds. The original problem which involves solving a fully nonlinear PDE in dimension two for the worst case scenario price, is reduced to solving a nonlinear PDE in dimension one and a linear PDE with source, which gives a tremendous computational advantage. Numerical experiments show that this approximation procedure performs very well, even in the regime of moderately slow varying stochastic bounds.
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中文摘要：
本文提出了具有随机界的不确定波动率模型。与常规的不确定波动率模型一样，我们只知道真正的模型存在于一系列渐进可测且有界的过程中，但不确定波动率不是使用两个确定性界，而是在其固有的随机波动率过程生成的两个随机界之间波动。这带来了更好的准确性，并与观察到的波动率路径一致，例如VIX作为代理。我们将正则摄动分析应用于最坏情形下的价格，并在慢变随机边界条件下推导了一阶近似。原始问题涉及求解最坏情况下价格的二维完全非线性偏微分方程，将其简化为求解一维非线性偏微分方程和带源的线性偏微分方程，这提供了巨大的计算优势。数值实验表明，即使在中等缓慢变化的随机边界条件下，这种近似方法也表现得很好。
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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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