Analytic valuation of European continuous-installment barrier options

Abstract

This study examines the valuation of European continuous-installment barrier options with dividend payments, under the classical Black-Scholes model. By using Mellin transform techniques, we derive the analytic integral solutions of European continuous-installment options with two types of barriers, so that the integral representations are decomposed into the value of the European barrier option and the premium of the early exercise installment. In the similar manner, the pricing of European continuous-installment barrier option which includes a rebate provision is investigated. Additionally, we investigate the effect of the free boundaries of European installment barrier options against barrier levels. Finally, by comparing the recursive integration method with the existing finite difference method - which is, in turn, based on the trinomial tree method as a benchmark - we analyze the accuracy and efficiency of the recursive integration method with respect to continuous-installment barrier options. (C) 2019 Elsevier B.V. All rights reserved.