Abstract
In this paper, we extend the SABO technique (Semi-Analytical method for Barrier Options), based on collocation Boundary Element Method (BEM), to the pricing of Barrier Options with payoff dependent on more than one asset. The efficiency and accuracy already revealed in the case of a single asset is confirmed by the presented numerical results.
Highlights
Introduction to the Differential Model ProblemPartial Differential Equations (PDEs) of Mathematical Physics model a huge variety of real-life problems, from science to engineering
Numerical results have been obtained by the code inserted in the Appendix A
It is obtained by SABO with ∆S = 0.125 2 and ∆t = 0.1
Summary
Partial Differential Equations (PDEs) of Mathematical Physics model a huge variety of real-life problems, from science to engineering. Equations that model physical phenomena have been reconsidered to interpret financial phenomena. PDEs in space–time variables, modeling the price of the most evolved financial products, need efficient techniques to be numerically solved. This work investigates the extensions of the so called SABO technique (Semi-Analytical method for Barrier Options), based on collocation Boundary Element Method (BEM) and applied so far for the numerical pricing of barrier options in a one dimensional asset framework [2]
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