Barrier option pricing under a Markov Regime switching diffusion model

Abstract

In this paper, we consider the pricing of barrier options under a Markov regime switching diffusion model. The proposed model incorporates structural changes in economic conditions and business and investment environments into the diffusion process, which captures some important stylized facts on asset returns such as asymmetry and heavy tail. Under the proposed model, we for the first time provide the closed-form upper and lower bounds of barrier options, and those bounds can be also improved systemically to obtain tighter bounds. By implementing extensive numerical experiments and fitting the proposed model to S&P 500, we present that the derived solution is highly effective and tight, and our work substantially extends the existing studies.