Valuation of American options under the CGMY model

Abstract

In the present work, we concentrate on the analytical study of American options under the CGMY process. The decomposition formula of the American option and the integral equation for the optimal-exercise boundary are established in explicit forms. Moreover, an analytical approximation formula is obtained for the American value. This approximation is valid when time to maturity is either very short or very long. Numerical simulations are provided for European options, optimal-exercise prices and approximate values for American options.

Keywords:

• CGMY model
• American option
• Decomposition formula
• Optimal-exercise boundary
• Approximate solution

JEL Classification:

• G12

Acknowledgements

Both authors would like to thank three anonymous reviewers and one editor for their invaluable comments and suggestions, which improved the manuscript a lot and made it more readable.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Y. Li was supported in part by the General Research Funds from Hong Kong Research Grants Council [grant number 201513], [grant number 1230515].