Multi-piecewise linear double barrier options

Abstract

A double barrier option offers diverse speculation and risk management opportunities due to its exotic characteristics. An avenue for enhancing its functionality involves considering double barriers with non-standard shapes, moving beyond the conventional flat structure. This paper introduces a multi-piecewise linear double barrier option and derives an explicit pricing formula for it grounded in the analytical probability that the underlying process does not breach the multi-piecewise linear double boundary. Through numerical illustrations, we explore how the configuration of the double barrier influences the option prices.