A series representation for the Black-Scholes formula

TL;DR

This paper introduces a new series representation for the European Black-Scholes call option formula, providing a more efficient and universally applicable approximation method across different market conditions.

Contribution

It generalizes and refines existing approximations, offering an efficient series representation that works in all market configurations.

Findings

The series representation improves computational efficiency.

It accurately approximates the Black-Scholes call in various market scenarios.

The method outperforms previous approximations in terms of accuracy.

Abstract

We prove and test an efficient series representation for the European Black-Scholes call, which generalizes and refines previously known approximations, and works in every market configuration.