An accurate approximation to barrier option prices with discrete fixed-amount dividends: Nonlinear dynamics

Abstract

While the asset usually pays discrete fixed-amount dividend in real markets, it is still an open problem on how to accurately and efficiently value barrier options under such circumstances where the underlying price process becomes nonlinear. This paper presents an accurate analytical approximation for barrier option prices, which can be applied no matter the number of dividends that are to be paid during the lifetime of the option contract. The resulting formula only involves the multivariate normal distribution function, which is very efficient to implement in practice.