1. Evaluating Natural Resource Investments: A Dynamic Option Simulation Approach Chung-Gee Lin Dept. of Business Mathematics Soochow University, Taiwan 2004 NTU International Conference on Finance

2. 1. Introduction  Natural resource investment (copper mine)  Net Present Value (NPV)  Managerial flexibilities: embedded options  Real Options approach  Dynamic Option Simulation (DOS)  Numerical analyses

3. Natural Resource Investments  Brennan and Schwartz (1985)  Castillo-Ramirez(1999)  Copper mine Temporary closure Reopen Abortion

4. Price a Complex Real Option  Multi-variable  Early exercise  Several embedded options  Finite reserves  Pricing ?

5.  Tree models  Cox, Ross, and Rubinstein (CRR, 1979)  Finite difference methods  Brennan and Schwartz (1978)  Monte Carlo simulations  Boyle (1977) Financial Numerical Methods

6.  LSM (Longstaff and Schwartz, 2001)  Multi-variable  Early exercise  Several embedded options  Dynamic programming  Finite reserves Dynamic Option Simulation (DOS)

7. 2. The Model  2.1 The stochastic variable processes

8.  Holding value Holding value > Early exercise value → Holding Holding value < Early exercise value → Exercise 2.2 The LSM

9. Copper Mine Holding Value  LSM

10. 3.3 DOS – Dynamic Programming N = 45 years, m = 15 years, decision frequency = once/year

11. DOS Steps  【 Step 1 】  【 Step 2 】  【 Step 3 】

12. The Embedded Options  Temporary closure  Open at q 1 (normal mining speed)  Abortion  Open at q 2 (faster mining speed)

13. Acceleration Options

14. 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

16. 3.1 The Values of Copper Mines and Embedded Options

17. 3.2 The Values of Copper Mines and Acceleration Options under Multi-variable

18. 3.3 Interest Rate Effects

19. 4. Conclusions  DOS  Copper mine values  Managerial flexibilities: embedded options  Acceleration Options  Interest rate effects

20. Comments and Suggestions are very welcome Chung-Gee Lin Dept. of Business Mathematics Soochow University, Taiwan Tel : +886-2- 2311-1531 ext. 3629 Fax : +886-2- 2381-2510 E-mail: cglin@bmath.scu.edu.tw