Barrier options and lumpy dividends

Abstract

We study the pricing of barrier options on stocks with lumpy dividends. By extending the European option methodology presented in Haug, Haug, and Lewis (2003), we show that in the Black–Scholes model with a single dividend payment, barrier option prices can be expressed in terms of well‐behaved one‐dimensional integrals that can be evaluated very rapidly. With multiple dividend payments, the price integrals are more involved, but we show that for the down‐and‐out call option a simple approximation method gives accurate results. Copyright © 2009 Wilmott Magazine Ltd