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Cubic B-Spline Collocation Method for Pricing Path Dependent Options

  • Geraldine Tour
  • Désiré Yannick Tangman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8584)

Abstract

We consider an efficient pricing method based on the cubic B-spline collocation method in which the approximation to the exact solution can be expressed as a linear combination of cubic B-spline basis functions. An earlier work has proposed to use such technique to solve the generalised Black–Scholes PDE to price European options only. In this work, we extend the application of the B-spline collocation method to price path-dependent options such as American, Barrier and Asian options under the Black–Scholes model. Our numerical results show that the new scheme is a method of choice for option pricing. Indeed the scheme has the same computational complexity as the standard second order finite difference scheme since they both require the solution of tridiagonal linear systems. However our numerical experiments reveal that the B-spline collocation method is more accurate in the infinity norm when solving convectively dominated financial problems and yields second order convergent prices and hedging parameters for both continuous and discretely sampled path-dependent options.

Keywords

collocation method cubic B-splines basis functions path-dependent option pricing 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Geraldine Tour
    • 1
  • Désiré Yannick Tangman
    • 1
  1. 1.Department of MathematicsUniversity of MauritiusRéduitMauritius

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