Evaluating Natural Resource Investments:

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2004 NTU International Conference on Finance

• Evaluating Natural Resource Investments
• A Dynamic Option Simulation Approach
• Chung-Gee Lin
• Dept. of Business Mathematics
• Soochow University, Taiwan

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1. Introduction

• Natural resource investment (copper mine)
• Net Present Value (NPV)
• Managerial flexibilities embedded options
• Real Options approach
• Dynamic Option Simulation (DOS)
• Numerical analyses

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Natural Resource Investments

• Brennan and Schwartz (1985)
• Castillo-Ramirez(1999)
• Copper mine
• Temporary closure
• Reopen
• Abortion

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Price a Complex Real Option

• Multi-variable
• Early exercise
• Several embedded options
• Finite reserves
• Pricing ?

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Financial Numerical Methods

• Tree models
• Cox, Ross, and Rubinstein (CRR, 1979)
• Finite difference methods
• Brennan and Schwartz (1978)
• Monte Carlo simulations
• Boyle (1977)

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Dynamic Option Simulation (DOS)

• LSM (Longstaff and Schwartz, 2001)
• Multi-variable
• Early exercise
• Several embedded options
• Dynamic programming
• Finite reserves

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2. The Model

• 2.1 The stochastic variable processes

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2.2 The LSM

• Holding value
• Holding value gt Early exercise value ? Holding
• Holding value lt Early exercise value ? Exercise

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Copper Mine Holding Value

• LSM

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3.3 DOS Dynamic Programming

• N 45 years , m 15 years, decision frequency
  once/year

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DOS Steps

• ?Step 1?
• ?Step 2?
• ?Step 3?

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The Embedded Options

• Temporary closure
• Open at q1 (normal mining speed)
• Abortion
• Open at q2 (faster mining speed)

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Acceleration Options
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3. Numerical Analyses

• The value of a copper mine
• The values of embedded options
• Under a multi-variable condition
• The value of a copper mine
• The values of Acceleration Options
• Interest rate effects

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3.1 The Values of Copper Mines and Embedded
Options
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3.2 The Values of Copper Mines and Acceleration
Options under Multi-variable
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3.3 Interest Rate Effects
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4. Conclusions

• DOS
• Copper mine values
• Managerial flexibilities embedded options
• Acceleration Options
• Interest rate effects

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Comments and Suggestions are very welcome

• Chung-Gee Lin    
• Dept. of Business Mathematics
• Soochow University, Taiwan
• Tel [phone] ext. 3629Fax 886-2-
  2381-2510     
• E-mail cglin_at_bmath.scu.edu.tw