European Options in BS Markets

  • Norbert Hilber
  • Oleg Reichmann
  • Christoph Schwab
  • Christoph Winter
Part of the Springer Finance book series (FINANCE)


In the last chapters, we explained various methods to solve partial differential equations. These methods are now applied to obtain the price of a European option. We assume that the stock price follows a geometric Brownian motion and show that the option price satisfies a parabolic PDE. The unbounded log-price domain is localized to a bounded domain and the error incurred by the truncation is estimated. It is shown that the variational formulation has a unique solution and the discretization schemes for finite element and finite differences are derived. Furthermore, we describe extensions of the Black–Scholes model, like the constant elasticity of variance (CEV) and the local volatility model.


Bilinear Form Infinitesimal Generator Geometric Brownian Motion European Option Barrier Option 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Norbert Hilber
    • 1
  • Oleg Reichmann
    • 2
  • Christoph Schwab
    • 2
  • Christoph Winter
    • 3
  1. 1.Dept. for Banking, Finance, Insurance, School of Management and LawZurich University of Applied SciencesWinterthurSwitzerland
  2. 2.Seminar for Applied MathematicsSwiss Federal Institute of Technology (ETH)ZurichSwitzerland
  3. 3.Allianz Deutschland AGMunichGermany

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