Non-Probabilistic Jump Modelling for Financial Derivatives

  • D. Bakstein
  • P. Wilmott
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)


This paper applies the uncertain nonlinear parameter approach, originally by Avellaneda et al. and Lyons, to model non-local changes in financial variables and the resulting impact on portfolios of derivatives and their underlying assets. It formulates the non-probabilistic uncertainty assumptions as a governing system of nonlinear PDEs about both the spatial and the time dimensions of the variables. The solution technique can be decomposed as a control problem for the former and a free-boundary problem for the latter. It is shown that, modelled in a non-probabilistic way any jump in a variable can be treated in the same manner as a dividend on equity.


Option Price Financial Derivative Dividend Announcement Vanilla Option Static Hedge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • D. Bakstein
    • 1
  • P. Wilmott
    • 1
  1. 1.Mathematical InstituteOxford Centre for Industrial and Applied MathematicsOxfordUK

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