Analytic solution for American barrier options with two barriers

This paper concerns American barrier options with two barriers. Standard American Options are difficult to price but there exist good numerical or analytical approximation methods. The situation is different for American barrier options. These options cease to exist or come into being if some price barrier is hit during the option's life. The paper studies analytic valuation of American barrier options with two barriers where the barriers become active by turns. In this paper, analytic valuation formulas for these options are derived by using both constant and exponential barriers for optimal early exercise policies.