Reconstructing local volatility using total variation

详细信息    查看全文

• 作者：Rui Yan Zhang ; Fang Fang Xu ; Jian Chao Huang
• 关键词：Volatility smile ; Dupire’s equation ; finite difference ; optimization ; multigrid method
• 刊名：Acta Mathematica Sinica, English Series
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：2
• 页码：263-277
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1439-7617
• 卷排序：33

文摘

The aim of this paper is to identify the volatility function in Dupire’s equation from given option prices. This inverse problem is formulated as an infinite-dimensional minimization problem with PDE constraints. The computational cost of solving the discretized problem on a fine discretization level is expensive. A multi-grid method is proposed to explore the hierarchical structures of discretized problems on different levels. Computational examples are presented to demonstrate the efficiency of our method.