障礙選擇權是市場上廣為流行之奇異選擇權。連續性障礙選擇權雖已發展出十分成熟之評價模型，但實務上，障礙選擇權卻大多為離散式之觀察點，以連續性模型估算離散式選擇權，將導致巨大之誤差。三項式格子點(Trinomial Lattice)及有限元素法雖可用以評價單一資產障礙選擇權，卻分別受限於結構式網格(Structured Mesh)及耗時等缺點，且易產生”Barrier-too-close”的問題。而將多重資產選擇權加上離散式障礙觀察點時，上述之方法，實務上將幾乎無法應用於其評價。
本研究利用變數變換將較為複雜的Parabolic partial differential equation轉換成線性同質方程式(Linear homogeneous equation)，因此可使用積分法(Integral Method)獲得十分精確之數值解。而利用越過障礙檢查點及分段回溯積分之觀點不但解決了一般數值方法面臨Barrier-too-close之問題；更讓演算時間隨著離散式障礙次數之增加呈線性成長而非一般數值方法演算時間呈指數成長。此外，當離散式障礙選擇權加上邊界限制條件時，積分法亦可被延伸成邊界元素法(Boundary Element Method)來求取精確數值解。
最後，以(up and out)兩資產離散式障礙選擇權作實例驗證，並針對各個參數作敏感性分析。

This study examines the valuation of multi-asset discrete barrier option by using recursive integral method and concept of jumping over the barrier price. An accurate solution for the PDE (Partial Differential Equation) requires a fine mesh near the discrete barriers, but when discrete barriers are applied to multiple assets, an accurate solution can barely be achieved with finite difference method and produce “barrier-too-close” problem easily. When the parabolic PDE is transformed into a Linear Homogeneous Equation, the integral method is a highly efficient method for finding an accurate numerical solution for the PDE. Beside, the recursive integral method and concept of jumping over barrier price not only solve the “barrier-too-close” problem, but also save the computational time. Furthermore, when free boundary constraints are introduced into the specifications of discrete barrier option, the integral method can be extended into the B.E.M (Boundary Element Method) for finding an extremely accurate solution for it. Finally, the method is used to value the (up and out) two-asset discrete barrier option, and sensitive analysis for parameters is presented.

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