數位選擇權是一市面上常見的新奇選擇權，由於為了滿足不同投資者的需求，選擇權的商品開始多樣化，因此本文將此選擇權商品加以變化加上障礙價格變成雙邊界障礙數位選擇權，討論其選擇權的定價，並提出與期望值方式訂價之差異。
　　本文以Black-Scholes定價理論為基礎，從Black-Scholes模型中推導方程式，接著轉變成熱傳導方程，再解此含有邊界及初始值的偏微分方程問題，並利用數值方法－邊界元素法來評價雙邊界障礙數位選擇權。接著，以股票期望報酬率以及股票觸碰特定價格觀點做期望值之計算。　　
　　最後從數值例中觀察出雙邊界障礙數位選擇權受障礙價格變動的明顯影響，且發現標的股其波動率越大者選擇權價格越高，波動率越小者選擇權價格越低；以及，無風險利率的高低，影響選擇權的價值。並發現以股票期望報酬率計算期望值之結果與前者相比價格會略高。

　　Digital option is one kind of exotic option in the market. In order to meet different investor demands for commodities it began to diversify options. So this text change this option with double barriers to discuss its pricing, and made way with the expected price difference.
　　This text base on Black-Scholes pricing theory, and from the Black-Scholes model equations are derived and then transformed into heat equation. And then we understand this with the boundary and initial value problems of partial differential equations, and use the numerical methods - Boundary Element Method to evaluate the Double Touch Barrier Digital Options. Then, with the expected rate of return and the stock to touch a specific price point to do the expected value.
　　Finally, from the numerical example observe double touch barrier digital option have the significant effect by the barrier interval. Found that the greater volatility of its option prices were higher, the smaller the volatility of its option prices were lower; as well, risk-free interest rate level, affect the option value. And found the expected value with the expected rate of return results slightly higher prices than the former.

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