On expansions for the Black-Scholes prices and hedge parameters

TL;DR

This paper introduces new uniformly convergent series formulas for European option prices and hedge parameters in the Black-Scholes model, improving approximation accuracy and providing convergence bounds.

Contribution

It presents generalized series formulas for option prices and Greeks, with convergence analysis, enhancing computational methods in financial modeling.

Findings

New series formulas for option prices and Greeks

Uniform convergence with explicit bounds

Improved accuracy over previous approximations

Abstract

We derive new formulas for the price of the European call and put options in the Black-Scholes model, under the form of uniformly convergent series generalizing previously known approximations. We also provide precise boundaries for the convergence speed and apply the results to the calculation of hedge parameters (Greeks).