The boundary value formulation of the Asian call option

  • J. Hugger
Conference paper


Financial instruments are normall y modelled in stochastic terms (Ito or Stratonovich formulation). This article is an attempt to present the modelling process from an Ito stochastic model to an analytical boundary value problem model. The presentation is given in analytical terms with a minimum of reference to stochastic theory and entirely without financial heuristics, for one particular financial instrument called the Asian option (in particular the fixed strike asian call option with continuous arithmetic average). The end result is a convection diffusion-type problem in two space-like dimensions (stock price and average) plus one time dimension.


Risky Asset Financial Instrument Contingent Claim Deterministic Function Continuous Average 


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  1. [1]
    Kwok, Y.-K. (1998): Mathematical models of financial derivatives. Springer, BerlinMATHGoogle Scholar
  2. [2]
    Hugger, J. (2002): Wellposedness of the boundary value formulation of the Asian cell option. International workshop on computational codes: the technological aspects of mathematics. Politecnico di Bari, submittedGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • J. Hugger
    • 1
    • 2
  1. 1.Dipartimento di Matematica “Ennio De Giorgi”Università degli StudiLecceItaly
  2. 2.Institute for Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark

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