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

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.