1. Explicit Option Pricing Formula for A Mean-Reverting Asset Anatoliy Swishchuk “Lunch at the Lab” Talk March 10, 2005

2. Outline Mean-Reverting Asset Model (MRAM) Explicit Solution for MRAM Explicit Option Pricing Formula for European Call Option under Physical Measure Mean-Reverting Risk-Neutral Asset Model (MRRNAM) Explicit Solution for MRRNAM Explicit Option Pricing Formula for European Call Option under Risk-Neutral Measure Numerical Example: AECO Natural Gas Index (1/05/98-30/04/99)

3. Mean-Reverting Asset Model (MRAM)

4. Explicit Solution for MRAM

5. Idea: Change of Time. I.

6. Idea: Change of Time. II.

7. Properties of the Process

8. Properties of Mean-Reverting Asset

9. Explicit Option Pricing Formula for European Call Option under Physical Measure

10. Parameters:

11. Mean-Reverting Risk-Neutral Asset Model (MRRNAM)

12. Transformations:

13. Explicit Solution for MRRNAM

14. Properties of the Process

15. Properties of MRRNAM

16. Explicit Option Pricing Formula for European Call Option under Risk-Neutral Measure

17. Numerical Example: AECO Natural Gas Index (1 May 1998-30 April 1999)