以有限差分法評價多期公共建設投資

Abstract

序列複合選擇權存在於當一個投資案擁有階段性的開發順序，且業主有權力參考上一階段 的成功與否來決定繼續投資下一階段或是放棄的時候。複合選擇買權本質上是由一個買權加上一 個買權所組成，而序列複合選擇權的意思則是一連串的複合選擇權。序列複合權對於評價土木工 程的多期投資開發工程非常有幫助。一般呈現網路型態之公用事業或基礎建設如捷運系統、瓦斯 管網、電信固網、區域下水道工程等皆為常見的多期開發投資案。Huang and Pi (2009)首先提供了 解析解解法來評價多期公共建設投資案(multi-stage infrastructure projects)，且包含了在早期階段的 特定資產(dedicated assets)投資問題。Huang and Pi(2011)進一步把多期投資之模型延伸應用在投資 計畫面臨市場競爭與技術汰換之問題上。 雖然Huang and Pi (2009, 2011)的研究可以應用在數種類型的公共建設投資案，但解析解的計 算過程複雜且必須遵循某些特定限制才能求解。在此次研究中，我們將採用與解析解不同的評價 近似法。將數值方法應用在評價多期公共建設投資案上。且利用幾種不同的有限差分法(Finite difference method)發展出幾個評價模型來評價多期公共建設投資案，並推導穩定度分析以及為了 數值方法的求解而發展一套演算法以計算。最後，我們將會利用一個真實的多期公共建設投資案 例來做為此方法的應用，以比較模型之間的效度及精度。

A sequential compound call option (SCCO) exists when a project has multiple phases and the investor has the option to whether invest the later phases. The investment decisions of the later phases depend on if the investments of the previous phases are successful or not. In essence, a compound option is a call option on a call option, and an SCCO is a sequence of compound options. Sequential compound options are useful for the valuation of multiple-stage investments in civil engineering. These investments include sewerage systems, gas-supply pipeline networks, MRT systems, and other network-type utilities or infrastructure projects. Huang and Pi (2009) first provide an analytical solution for the valuation of multi-stage infrastructure projects involving dedicated asset investments in earlier stages. Huang and Pi (2010) extend their previous for the valuation of multi-stage infrastructure projects subjected market competition and technological obsolescence. Even though Huang and Pi’s (2009, 2011) works are applicable in several types of infrastructure investments, the search for analytical solution is not an easy process and is necessarily subjected to many foreseeable constraints. In this research, we adapt a different valuation approach. Numerical methods are applied for the valuation of multiple-stage infrastructure investments. Using various finite difference methods, valuation models are developed for multiple-stage infrastructure investments. Stability analyses are conducted, and algorithms for the numerical implementations are developed. Finally, the efficiency and accuracy of these methods are compared using a real-world multiple-stage infrastructure investment project as an application.