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Control-theoretic framework for a quasi-Newton local volatility surface inversion

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  • Gabriel Turinici

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

Abstract

We investigate in this paper the recovery of the local volatility surface in a parametric framework similar to that of Coleman, Li and Verma [4]. The quality of a surface is assessed through a functional which is optimized; the specificity of the approach is to separate the optimization on the parametric space (performed with any suitable optimization algorithm) from the computation of the functional where we use an adjoint formulation similar to that of the optimal control; the procedure can thus incorporate information from any derivative contract compatible with the adjoint approach. The procedure was implemented and was shown to perform satisfactory on real-world data.

Suggested Citation

  • Gabriel Turinici, 2008. "Control-theoretic framework for a quasi-Newton local volatility surface inversion," Post-Print hal-00298960, HAL.
  • Handle: RePEc:hal:journl:hal-00298960 Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00298960
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