FINITE DIFFERENCE METHOD TO THE SEQUENTIAL COMPOUND CALL OPTION VALUATION PROBLEM FOR MULTISTAGE INFRASTRUCTURE INVESTMENTS

以有限差分法求解多期公共建設投資方案的序列複合選擇權評價

黃玉霖(Yu-Lin Huang) ； 林岑縉(Tsen-Chin Lin)

《中國土木水利工程學刊》 32卷1期 (2020/03) Pp. 35-47

https://doi.org/10.6652/JoCICHE.202003_32(1).0004

摘要

Solving the problem of sequential compound call option valuation is crucial to making decisions related to investment in multistage infrastructure projects. However, the analytical method solution to the sequential compound call option valuation problem is complex and inefficient. Three finite difference methods are proposed for obtaining faster solutions to the sequential compound call option valuation problem. The explicit, implicit and Crank-Nicolson methods are provided, and a real-world numerical case study is presented to illustrate the applicability and performance of the methods. The proposed methods can produce desirable valuation outcomes in terms of speed and accuracy under certain conditions. In particular, the Crank-Nicolson method is optimal for conducting valuations when only yearly asset data are available. When weekly or daily data are available and asset volatility is lower, the explicit method tends to perform more favorably. When the observed asset volatility is higher, the implicit method and the Crank-Nicolson method tend to be more accurate. Moreover, the implicit method and the Crank-Nicolson method are unconditionally stable, and therefore, at the cost of increased computation time, an appropriate maximum asset value can be set and a small grid design can be used to improve the accuracy.

關鍵字

finite difference method ； sequential compound call option ； multistage infrastructure

並列摘要

解決序列複合選擇權評價問題對於多期公共建設投資案之可行性來說是非常重要的。然而，現存之封閉解對於此類專案來說過於複雜且無效率。有鑑於此，本研究利用工程領域常用之有限差分法來建立更有效率且簡單之序列複合選擇權模型。本研究經由真實案例驗證了顯式法、隱式法以及Crank-Nicolson法可解決此類序列複合選擇權評價問題，並在特定情況下提供了更佳的準確度與計算速度。當以年為單位觀察時，Crank-Nicolson法在準確度上表現較好，在以週或日為單位觀察時，且資產波動度較低時，顯式法提供更好的結果。然而，當資產波動度較高時，隱式法和Crank-Nicolson法之結果較為準確。

並列關鍵字

有限差分法 ； 序列複合選擇權 ； 多期公共建設投資