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.
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Supported by NSFC (Grant No. 11322109) and Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (Grant No. 2015RCJJ056)
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Zhang, R.Y., Xu, F.F. & Huang, J.C. Reconstructing local volatility using total variation. Acta. Math. Sin.-English Ser. 33, 263–277 (2017). https://doi.org/10.1007/s10114-017-5178-7
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DOI: https://doi.org/10.1007/s10114-017-5178-7