Multinode Shepard collocation method for pricing of financial derivatives

TL;DR

This paper introduces a multinode Shepard collocation method combined with backward difference temporal discretization to solve the two-dimensional Black-Scholes equation, demonstrating improved accuracy and efficiency in pricing financial derivatives.

Contribution

The paper presents a novel numerical approach that integrates multinode Shepard approximation with backward difference methods for better solving the Black-Scholes PDE.

Findings

Demonstrates high accuracy in numerical experiments

Shows effectiveness in pricing complex derivatives

Provides a stable and efficient computational method

Abstract

This paper explores the use of the multinode Shepard method for the numerical solution of the two-dimensional Black-Scholes equation. The proposed approach integrates a spatial approximation via the multinode Shepard operator with a temporal discretization based on the Backward Difference Formula. Numerical experiments are presented to demonstrate the accuracy and effectiveness of the method.