Pricing near the barrier: the case of discrete knock-out options

Manfred Steiner and Martin Wallmeier, Reinhold Hafner

Abstract

ABSTRACT

This paper investigates the pricing of discrete knock-out options with tree methods, with special emphasis on stock prices close to the barrier. As is well known, the naive application of the binomial model can result in erroneous prices, even if the number of time steps is large. A correction technique for the binomial and trinomial model that is applicable to different types of barrier options is developed. The results of simulations show that, with this technique, a small number of time steps suffices to obtain accurate option prices, even if volatility is high and the barrier lies near the current stock price. This is an important advantage compared with commonly used pricing methods. In addition, the results with respect to speed and accuracy turn out to be robust over a wide range of option parameters.