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dc.contributor.authorZhang, K.
dc.contributor.authorTeo, Kok Lay
dc.date.accessioned2017-01-30T10:31:31Z
dc.date.available2017-01-30T10:31:31Z
dc.date.created2015-08-03T20:01:39Z
dc.date.issued2015
dc.identifier.citationZhang, K. and Teo, K.L. 2015. A penalty-based method from reconstructing smooth local volatility surface from American options. Journal of Industrial and Management Optimization (JIMO). 11 (2): pp. 631-644.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/3463
dc.identifier.doi10.3934/jimo.2015.11.631
dc.description.abstract

This paper is devoted to develop a robust penalty-based method of reconstructing smooth local volatility surface from the observed American option prices. This reconstruction problem is posed as an inverse problem: given a nite set of observed American option prices, nd a local volatility function such that the theoretical option prices matches the observed ones optimally with respect to a prescribed performance criterion. The theoretical American option prices are governed by a set of partial dierential complementarity problems (PDCP). We propose a penalty-based numerical method for the solution of the PDCP. Typically, the reconstruction problem is ill-posed and a bicubic spline regularization technique is thus proposed to overcome this diculty. We apply a gradient-based optimization algorithm to solve this nonlinear optimization problem, where the Jacobian of the cost function is computed via nite dierence approximation. Two numerical experiments: a synthetic American put option example and a real market American put option example, are performed to show the robustness and eectiveness of the proposed method to reconstructing the unknown volatility surface.

dc.publisherAmerican Institute of Mathematical Sciences
dc.titleA penalty-based method from reconstructing smooth local volatility surface from American options
dc.typeJournal Article
dcterms.source.volume11
dcterms.source.number2
dcterms.source.startPage631
dcterms.source.endPage644
dcterms.source.issn1553-166X
dcterms.source.titleJournal of Industrial and Management Optimization (JIMO)
curtin.departmentDepartment of Mathematics and Statistics
curtin.accessStatusOpen access via publisher


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