Explicit Option Pricing Formula for
A Mean-Reverting Asset
Anatoliy Swishchuk
“Lunch at the Lab” Talk
March 10, 2005
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)
Mean-Reverting Asset Model (MRAM)
Explicit Solution for MRAM
Idea: Change of Time. I.
Idea: Change of Time. II.
Properties of the Process
Properties of Mean-Reverting Asset
Explicit Option Pricing Formula for European
Call Option under Physical Measure
Parameters:
Mean-Reverting Risk-Neutral Asset Model
(MRRNAM)
Transformations:
Explicit Solution for MRRNAM
Properties of the Process
Properties of MRRNAM
Explicit Option Pricing Formula for European
Call Option under Risk-Neutral Measure
Numerical Example: AECO Natural Gas Index
(1 May 1998-30 April 1999)