多層序列買權之敏感度分析與公共工程投資應用

Abstract

多期公共工程是複雜的公共投資計畫。特別是，在公共工程民營化過程中，民間投資人除了 保留投資彈性，還必須審慎處理特定資產(dedicated assets)投資以及技術汰舊風險等問題。但是， 傳統的投資評估方法，包括現金流量折現法(Discounted Cash Flow Method)和決策樹(Decision Tree)等，都無法處理這些複雜計畫的投資評估問題；甚至於比較傳統的實質選擇權模型 (Real-option Models)，也都無法提供合理的答案。 鑑於民營公共工程投資對國家社會經濟之重要性，本研究將深入探討多期序列複合買權 (multifold sequential compound call options)在多期公共工程投資評估之應用。本研究將針對這種新 奇實質選擇權評價模型中的執行價格及股息發放比率，進行敏感度分析，推導Kappa(∂C / ∂k)與 Quoppa(∂C / ∂q)之解析解，並將結果應用在特定資產及技術汰舊風險之評價問題上。同時，本研 究將處裡多期序列複合買權複雜的金融計算問題，開發多期公共工程投資評估軟體，以利實務應 用。 透過多期序列複合買權評價模型來評估多期公共工程投資，本研究將在複雜專案評估 (evaluation of complex projects)上做出貢獻。同時，由於衍生性金融商品敏感度分析著重金融選擇 權避險策略之應用，在工程投資評估與決策分析之應用有限。本研究推導Kappa 與Quoppa，並將 結果應用在重要的工程投資決策上，將有助於了解實質選擇權的內涵，以及實質選擇權與一般衍 生性金融商品間的基本差異。

Multi-stage public works are complex public investment projects. In particular, in the privatization of the works, private investors not only need to secure the rights for flexible investment decision making; they also have to deal with care the issues of dedicated assets and technological obsolescence risk. However, traditional project evaluation approaches, such as the discounted cash flow method and decision trees, fail to deal with those more complex valuation issues. Even traditional real-option models cannot provide sensible answers. Because privatized public works projects are vital to the Nation’s social and economic developments, this research aims to study in depth the application of multi-fold sequential compound call options (SCO) in the evaluation of multi-stage privatized public works investment. Especially, the study will derive analytical solutions for the sensitivities of real-option values to the exercise price and the dividend and debt interest payout rate, which are called Kappa (∂C / ∂k) and Quoppa (∂C / ∂q) respectively. The sensitivities or the Greek Letters can be applied to evaluate dedicated asset investment as well as technological obsolescence risk. Meanwhile, this research will deal with the complex financial computation issues involved in the SCO valuation model, and develop a computer program for real-world applications. Evaluating multistage public works investment projects through SCO, this research will make a contribution to the evaluation of complex projects in general. In addition, since the sensitivity analysis of derivative securities focuses on the application of hedging strategies, it is not very useful for engineering investment evaluation and decision-making. By deriving Kappa and Quoppa and applying them to engineering investment decisions, this research will demonstrate the very nature of real options as well as some of the fundamental differences between real options and financial derivatives.