Closed-Form Approximate Solutions of Window Barrier Options with Term-Structure Volatility and Interest Rates Using the Boundary Integral Method

Yi-Long Hsiao^*

Department of Finance, National Dong Hwa University, Hualien.

DOI: 10.4236/jmf.2012.24032                

Abstract

In this study we propose an approach to solve a partial differential equation (PDE), the boundary integral method, for the valuation of both discrete and continuous window barrier options, as well as multi-window barrier options within a deterministic term structure of volatility and interest rates. Numerical results reveal that the proposed method yields rapid and highly accurate closed-form approximate solutions. In addition, the term structure will have a significant impact on the valuation.

Keywords

Window Barrier Option; Integral Method; Integral Representation; Green’s Function; PDE Approach

Conflicts of Interest

The authors declare no conflicts of interest.

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