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

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.