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Pricing of European options using a cubic spline collocation method

A. Serghini, A. El hajaji, E.B. Mermri, K. Hilal


In this paper, we develop a new numerical method to price European options under the Black and Scholes model which is governed by a generalized Black-Scholes partial differential equation. We first propose the theta-method to discretize the temporal variable, resulting in a linear partial differential equation (PDE). To numerically solve this linear PDE, we develop and we analyze a new cubic spline collocation method for the spatial discretization. To solve the discretized linear system, we design a collocation method and we prove that the method is second order convergent. Numerical results are presented and compared with other collocation methods given in the literature.


Black-Scholes equation, european call options, spline collocation method.

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