An Accurate Pricing Formula for Vanilla Options in a Cash Dividend Framework with Linear Algorithmic Complexity

Abstract

The aim of this article is to provide a fast and efficient formula to price vanilla options in presence of cash dividends. Bos & Vandermark have provided a simple and intuitive formula but not really accurate for long maturities or for strikes far from the money. Many authors have proposed some accurate formula but with a polynomial (quadratic for Henry-Labordere) algorithmic complexity in the number of dividends. In this article we derive a formula whose accuracy is equivalent to that of Henry-Labordere but with a linear algorithmic complexity, preserving the call-put parity and the continuity of the vanilla price at each ex-dividend dates.