More stochastic expansions for the pricing of vanilla options with cash dividends

TL;DR

This paper introduces new stochastic expansion methods for pricing European vanilla options with discrete cash dividends, providing more robust approximations across various strikes and dividend dates.

Contribution

It develops alternative higher-order expansions based on Etore and Gobet's technique for more accurate option pricing with dividends.

Findings

More accurate pricing approximations for options with dividends.

Robust first, second, and third-order expansions.

Applicable across a wide range of strikes and dividend dates.

Abstract

There is no exact closed form formula for pricing of European options with discrete cash dividends under the model where the underlying asset price follows a piecewise lognormal process with jumps at dividend ex-dates. This paper presents alternative expansions based on the technique of Etore and Gobet, leading to more robust first, second and third-order expansions across the range of strikes and the range of dividend dates.