Pricing of Discretely Monitored Barrier Options - Improvement of an Approximation Formula

Abstract: There are many different methods for pricing discretely monitored barrier options. There is a trade-off, however, between speed and accuracy. The players on the financial markets would of course ideally want a method which is both exact and returns a price instantaneously. In this thesis we start from a fast, but on the other hand somewhat less accurate, approximation formula. It will be referred to as the 0.5826-approximation, and was introduced in 1997 by Broadie,Glasserman and Kou [1]. It is one of the option pricing formulas currently used by SunGard. The idea of the 0.5826-approximation is to use the analytical pricing formula for the corresponding continuously monitored barrier option, and to use an adjusted barrier in that formula to account for the decreased probability of a barrier hit. The purpose of this thesis is to improve the 0.5826-approximation for down-and-out call options with barrier less than or equal to the strike, and in particular to mitigate two problems.