A finite volume–alternating direction implicit method for the valuation of American options under the Heston model

ABSTRACT

A finite volume–alternating direction implicit method is proposed for numerical valuation of the American options under the Heston model. It is based on decoupling correlated stock price process and volatility process so that corresponding partial differential operator does not contain the mixed partial derivative term. Hence, the proposed method is numerically simple and fast. Numerical results are presented to examine the accuracy of the proposed method and to compare it with the others.

KEYWORDS:

• Options valuation
• finite volume method
• alternating direction implicit method
• Heston model

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65M08
• 91G20
• 91G60

Acknowledgements

The authors would like to thank the reviewers for their constructive comments that significantly improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.