A semi‐smooth Newton method for an inverse problem in option pricing | Zendy

Düring Bertram | Zendy

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A semi‐smooth Newton method for an inverse problem in option pricing

Author(s) -

Düring Bertram

Publication year - 2007

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.200700708

Subject(s) - sequential quadratic programming , newton's method , line search , mathematical optimization , dual (grammatical number) , quadratic programming , quadratic equation , mathematics , optimal control , set (abstract data type) , inverse , order (exchange) , volatility (finance) , computer science , finance , economics , nonlinear system , art , physics , geometry , computer security , literature , quantum mechanics , programming language , radius , econometrics

We present an optimal control approach using a Lagrangian framework to identify local volatility functions from given option prices. We employ a globalized sequential quadratic programming (SQP) algorithm and implement a line search strategy. The linear‐quadratic optimal control problems in each iteration are solved by a primal‐dual active set strategy which leads to a semi‐smooth Newton method. We present first‐ and second‐order analysis as well as numerical results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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