Various types of double-barrier options

Lawrence S. J. Luo

Abstract

ABSTRACT

Based on hitting probabilities of a Brownian motion derived by Sidenius (1998), this paper derives closed-form solutions for eight types of European-style double-barrier options. The results show that, in order to solve linearly all eight types of double-barrier options, formulas of at least two linearly independent double-barrier options must be given. This corrects a statement in the paper by Sidenius that any double-barrier options are linear combinations of double knock-out options, single-barrier options, and vanilla options. Error estimates for numerical valuation of double-barrier options are also derived in this paper. These estimates are more accurate and more reliable than those given by the methods used in other studies on double-barrier options.