在以往的文獻當中，大部分是以幾何布朗運動來模擬公司專案的現金流量，而其波動度則是以歷史的資料來設定一個常數波動度。但是現實上波動度並非是固定不變的，而且利用幾何布朗運動來模擬公司專案的現金流量也不能夠捕捉到現金流量不連續的跳動情況，本篇文章的模型是利用一個更一般化的隨機過程 Le ́vy 過程的框架來捕捉含有離散跳動情形的公司專案現金流量動態過程，並以Constant Elasticity of Variance (CEV)模擬變動的波動度。最後探討在Jump diffusion 模式加上CEV的實質選擇權模型之下的投資不確定性關係，並推導出公司專案的最適投資點。

Much of real options’ work assumes that the underlying variable follows a constant volatility geometric Brownian motion. This paper uses a more general assumption which is Le ́vy process framework and this paper chooses a specific case of Le ́vy process which is jump diffusion type model. We use jump diffusion type model with the constant elasticity of variance diffusion to examine the investment-uncertainty relationship in real options model. Finally we derive a solution for the critical investment value of a corporate’s projects.

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