Black–Scholes Option Pricing Model

  • Jürgen FrankeEmail author
  • Wolfgang Karl Härdle
  • Christian Matthias Hafner
Part of the Universitext book series (UTX)


Simple, generally accepted economic assumptions are insufficient to develop a rational option pricing theory. Assuming a perfect financial market (Section2.1) leads to elementary arbitrage relations which the options have to fulfill. While these relations can be used as a verification tool for sophisticated mathematical models, they do not provide an explicit option pricing function depending on parameters such as time, stock price and the options underlying parameters K, T. To obtain such a pricing function the value of the underlying financial instrument (stock, currency,...) has to be modelled. In general, the underlying instrument is assumed to follow a stochastic process either in discrete or in continuous time. While the latter is analytically easier to handle, the former, which we will consider as an approximation of a continuous time process for the time being, is particularly useful for numerical computations. In the second part of this text, the discrete time version will be discussed as a financial time series model.


Stock Price Option Price Call Option Implied Volatility Future Contract 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jürgen Franke
    • 1
    Email author
  • Wolfgang Karl Härdle
    • 2
    • 3
  • Christian Matthias Hafner
    • 4
  1. 1.FB MathematikTU KaiserslauternKaiserslauternGermany
  2. 2.Ladislaus von Bortkiewicz Chair of Statistics C.A.S.E. Centre for Applied Statistics and Economics School of Business and EconomicsHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Graduate Institute of StatisticsNational Central UniversityJhongliTaiwan
  4. 4.Inst. StatistiqueUniversité Catholique de LouvainLeuven-la-NeuveBelgium

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