ANALYSIS OF INVESTMENT UNCERTAINTY RELATIONSHIP UNDER A JUMP-DIFFUSION MODEL AND CONSTANT ELASTICITY OF VARIANCE PROCESS

在跳躍擴散和CEV模型下探討投資不確定性關係

陳妙盈(Miao-Ying Chen) ； 張傳章(Chuang-Chang Chang) ； 張竹萱(Chu-Hsuan Chang) ； 李世偉(Shi-Wei Li)

《中國統計學報》 54卷4期 (2016/12) Pp. 205-228

摘要

Applying the real options approach, this paper uses a jump-diffusion model with constant elasticity of variance (CEV) components by choosing a compound Poisson process to examine the investment opportunity. Through incorporation of unpredictable but sizeable changes in a firm's projected earnings, the jump-diffusion CEV model can depict the jump effect on earnings under investment uncertainty by modeling the constant volatility change over time, enabling evaluation of the probability that an investment will take place. Using the jump-diffusion CEV model, this study demonstrates that the critical investment value is an increasing function of jump size and a decreasing function of the CEV elasticity parameter. Furthermore, this paper shows that both the direction of the jump and jump frequency may influence the investment opportunity. Numerical results show that the probability of investment may increase when jumps are expected to be positive and more frequent in the earnings stream. Conversely, investment opportunity is likely to decrease with more frequent but negative jumps in expected cash flows.

關鍵字

Real options model ； CEV ； Investment ； Jump-diffusion process

並列摘要

本文建構在跳躍擴散和CEV模型下探討投資不確定性關係。由於公司的預期未來盈餘為不可預知的，故利用跳躍擴散CEV模型將可以更精確描述其波動變化，增加估計投資機會的準確性。在跳躍擴散CEV模型下，可以發現可投資的臨界值會是跳躍幅度的遞增函數及CEV模型參數的遞減函數，且跳躍方向和跳躍頻率皆可能會影響投資機會。數值分析結果顯示，當預期未來盈餘之跳躍為正值且頻率愈高時，投資機會隨之增加，相反的當預期未來盈餘之跳躍為負值時，投資機會可能隨之減少。

並列關鍵字

實質選擇權 ； CEV模型 ； 跳躍擴散模型

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