Computational Economics

, Volume 48, Issue 1, pp 131–145

A Numerical Method for Discrete Single Barrier Option Pricing with Time-Dependent Parameters

  • Rahman Farnoosh
  • Hamidreza Rezazadeh
  • Amirhossein Sobhani
  • M. Hossein Beheshti
Article

Abstract

In this article, the researchers obtained a recursive formula for the price of discrete single barrier option based on the Black–Scholes framework in which drift, dividend yield and volatility assumed as deterministic functions of time. With some general transformations, the partial differential equations (PDEs) corresponding to option value problem, in each monitoring time interval, were converted into well-known Black–Scholes PDE with constant coefficients. Finally, an innovative numerical approach was proposed to utilize the obtained recursive formula efficiently. Despite some claims, it has considerably low computational cost and could be competitive with the other introduced method. In addition, one advantage of this method, is that the Greeks of the contracts were also calculated.

Keywords

Barrier option Black–Scholes framework Discrete monitoring Time-dependent parameters Greeks 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Rahman Farnoosh
    • 1
  • Hamidreza Rezazadeh
    • 1
  • Amirhossein Sobhani
    • 1
  • M. Hossein Beheshti
    • 2
  1. 1.School of MathematicsIran University of Science and TechnologyTehranIran
  2. 2.Department of Mathematics, Varamin-Pishva BranchIslamic Azad universityVaraminIran

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