臺灣博碩士論文加值系統

天然資源開採之專案計畫評估，牽涉到複雜的評價問題。本研究以銅礦開採為例，考量現實天然資源開採計畫之特性，允許在特定時點，賦予此一計畫：暫時關閉、重新開採、提前放棄等選擇權。為了進一步令分析模式更契合現實情況，本文考慮多種影響天然資源評價的不確定因子：銅價、收益率(convenience yield)、生產成本、與無風險利率。其中，本文模型假設銅價可能因市場供需丕變，造成價格巨幅波動(Jumps)的情況。根據上述的定式，天然資源專案計畫分析，可視為多因子美式選擇權評價問題。
傳統上，企業考慮投資決策時所採用的資本預算方式一般為現金流量法中的淨現值法(Net Present Value, NPV)。然而NPV的適用性一直受到爭議。Dixit & Pindyck(1995)指出，NPV 法運用上雖然簡單，但其投資可回復與投資無法遞延的假設，與現實上有極大的出入，因為實際上，大部分的投資通常是：(1)投資為部分或完全不能收回的，(2)未來報酬是不確定性的，(3)投資者有選擇最適時間點(timing)投資的權利，亦即投資決策者可將計畫遞延以獲得更多資訊。由上述三點可之，實際上大部分的投資是不可逆轉的(irreversible)，而且是可遞延的(deferrable )。
由於現金流量法無法將投資計畫之中的選擇權價值納入模式，因此會有低估投資計畫的問題。為了有效評估實際的投資方案價值，以選擇權評價模式從事資本預算決策的評價，即實質選擇權方法(Real Options approach)，始可幫助投資人進行正確的投資決策。天然資源開採之專案計畫評估，為一多期實質選擇權問題，其中還包含了多重的實質選擇權，各個選擇權之間，彼此還有相關性問題存在，而且可以提前履約。由於模式過於複雜，企圖推導出封閉解(closed form solution)可說是緣木求魚。本文利用Longstaff & Schwartz(2001)所發展出的模擬法結合動態規劃，可以解決諸如：多重因子、提前履約、多期多重實質選擇權等問題，有效與正確地評估天然資源計畫的價值。

Natural resource project evaluation is a complex pricing problem. We take a copper mine valuation for example, which provides options of being closed, reopened, and abandoned with some finite frequencies. In order to construct a practical model, we considered several state variables that will influence the value of a copper mine, they are: copper price, convenience yield, production cost, and risk free interest rate. In addition, we assume the copper price will jump because of the great change of market demands and supplies.
Traditionally, an enterprise makes investment decision by using the net present value methodologies (NPV). However, the applicability of NPV is questionable, since there are many impractical assumptions under this method. Dixit & Pindyck(1995) pointed out that, in reality, most investments are (1) partially or totally recoverable, (2) with uncertain returns in the future, (3) have the right to defer. Unfortunately, the NPV does not conform to these rules.
Since the NPV does not consider the value of options, this methodology has the risk of undervaluing an investment. In order to evaluate the real value of an investment, applying the option pricing theory into investment decision, i.e. real options approach, can efficiently assist the investors to make the right decisions.
Natural resource investment evaluation is just like a multi-period, multiple real options problem. There are no closed form solutions to this problem because of its complexity, we applied the dynamic simulation methodology developed by Longstaff & Schwartz (2001) to copy with the pricing problems: multi-factors, early exercise, path dependent, multi-period, and multiple options. The methodology presented here can effectively evaluate a natural resource investment.

目錄
1.導論
1.1 研究動機……………………………………………………………………6
1.2 研究目的……………………………………………………………………7
1.3 研究架構……………………………………………………………………7
2.文獻回顧
2.1選擇權……………………………………………………………………….8
2.1.1選擇權的意義及種類………………………………………………....8
2.1.2選擇權的評價方法……………………………………………………9
2.1.3選擇權的發展…………………………………………………………10
2.2 實質選擇權………………………………………………………………….10
2.2.1實質選擇權之介紹……………………………………………………11
2.2.2實質選擇權的發展來源………………………………………………11
2.2.3實質選擇權的種類……………………………………………………12
2.2.4實質選擇權的應用及發展……………………………………………14
3.研究方法
3.1 蒙地卡羅最小平方法……………………………………………16
3.2利率期限結植(CIR)………………………………………………18
3.3 模型設定…………………………………………………………18
3.3.1單狀態變數………………………………………………………19
3.3.2動態選擇權模擬法(DOS)………………………………………20
3.3.3 衍生模型─四狀態變數………………………………………22
4.數值分析
4.1無選擇權下天然資源計劃………………………………………26
4.2不同狀態變數下天然資源計劃價………………………………27
4.3各種參數敏感度分析……………………………………………28
4.3.1銅價參數效率…………………………………………………28
4.3.2收益率參數效果………………………………………………29
4.3.3成本參數效果…………………………………………………30
4.3.4利率參數效果…………………………………………………30
4.3.5相關係數參數效果……………………………………………31
5.結論………………………………………………………………33

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