We will treat how to achieve great computational savings and accuracy in the evaluation of barrier options through Boundary Element Method (BEM). The proposed method applies to quite general pricing models. The only requirement is the knowledge of the characteristic function for the underlying asset distribution, usually available under general asset models. This paper serves as an introductory work to illustrate the implementation of BEM using numerical Fourier inverse transform of the characteristic function and to numerically show its stability and efficiency under simple frameworks such as the Black-Scholes model.
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