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- Title
Reconstructing local volatility using total variation.
- Authors
Zhang, Rui; Xu, Fang; Huang, Jian
- Abstract
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.
- Subjects
MARKET volatility; VARIATIONAL principles; DISCRETIZATION methods; FINITE differences; MATHEMATICAL optimization
- Publication
Acta Mathematica Sinica, 2017, Vol 33, Issue 2, p263
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-017-5178-7