Semi-Analytical method for the pricing of barrier options in case of time-dependent parameters (with Matlab® codes)

A Semi-Analytical method for pricing of Barrier Options (SABO) is presented. The method is based on the foundations of Boundary Integral Methods which is recast here for the application to barrier option pricing in the Black-Scholes model with time-dependent interest rate, volatility and dividend yield. The validity of the numerical method is illustrated by several numerical examples and comparisons.

Regularized singular boundary method for groundwater flow in a cofferdam

The boundary integral methods form one group of methods for solving differential equations. The boundary element method (BEM) is the basic method of this group. However, it requires the boundary mesh of elements and the evaluation of improper singular integrals, that arise due to fundamental solution singularity. Therefore, boundary meshless methods have recently have come into focus to remove these shortcomings. One of the most promising boundary collocation numerical schemes is the singular boundary method (SBM). To tackle the singularity of the fundamental solution, this method adopts the concept of original intensity factors (OIFs). The application of the proposed SBM scheme to groundwater flow in the cofferdam structure is presented and compared to the finite element method (FEM) solution.