Analytical approximation method of option pricing under geometric mean-reverting process

Abstract

This paper is concerned with analytical approximation for option pricing while the underlying asset price follows a geometric mean-reverting diffusion process, which is often used in real and commodity options. Two methods are developed, one employing the idea of Edgeworth series expansion and another based on Taylor series expansion. Numerical tests show that the second method significantly outperforms the first one, particularly for long-maturity options. In addition, we compare the analytical approximation prices with that obtained using an alternative log-normal model for commodities and find out for many cases the discrepancy in option prices is remarkable.

Keywords:

• option pricing
• geometric mean-reverting process
• analytical approximation
• Taylor series expansion
• Edgeworth series expansion

2000 AMS Subject Classifications :

• 41A58
• 60-08
• 65C20
• 91B70