An Efficient, and Fast Convergent Algorithm for Barrier Options

Abstract

A barrier option is an option whose payoff depends on whether the price path of the underlying asset ever reaches certain predetermined price levels called the barriers. A single- (double-) barrier option is a barrier option with one (two, respectively) barrier(s). No simple and exact closed-form pricing formula for double-barrier options has been reported in the literature. This paper proposes a novel tree model that can price both single- and double-barrier options efficiently and accurately. This tree model achieves the high efficiency by combinatorial techniques and numerical accuracy by hitting the barriers exactly. Numerical experiments are given to verify the superiority of our method.