Modeling Vanilla Option prices: A simulation study by an implicit method

TL;DR

This paper presents an implicit finite difference method to efficiently and accurately solve the Black-Scholes PDE for vanilla options, reducing computation time and error while maintaining second-order accuracy.

Contribution

It introduces a second-order accurate implicit discretization scheme for option pricing, validated against known analytical solutions, enhancing computational efficiency.

Findings

The implicit method achieves high accuracy with reduced errors.

The approach demonstrates computational efficiency for European options.

Second-order accuracy is confirmed through numerical experiments.

Abstract

Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized simultaneously. In this paper, the authors have solved the Black-Scholes equation by employing a reasonably accurate implicit method. Options with known analytic solutions have been evaluated. Furthermore, an overall second order accurate space and time discretization is proposed in this paper Keywords: Computational finance, implicit methods, finite differences, call/put options.