Rannacher time-marching with orthogonal spline collocation method for retrieving the discontinuous behavior of hedging parameters

Highlights：

• To demonstrate the feasibility of the proposed system, financially relevant irregular initial data-based problems are used.

• For problems with discontinuous derivative functions (Greeks in finance), the orthogonal spline collocation approach has been shown to be extremely accurate.

• The Rannacher time-marching scheme is shown to be superior to the backward Euler and Crank-Nicolson schemes in terms of computational cost and accuracy. Also it is sufficient to restore the expected behavior.

• An analysis of the current numerical scheme’s theoretical and numerical convergence is provided.

• The current research can be applied to the trading industry to reduce risk and control portfolios. In addition, the current scheme is simple to incorporate and apply to a variety of non-smooth initial data-based moving boundary value problems for future computational studies.