CCF approach for asymptotic option pricing under the CEV diffusion

Abstract

In the last two decades, the asymptotic expansion approach has become popular in mathematical finance because it enables us to obtain closed-form approximation formulae for many kinds of options within various kinds of financial models, such as local and stochastic volatility models. In this study, we propose an asymptotic expansion formula for the option price in a constant elasticity of variance model using the asymptotic expansion technique and Fourier analysis. This approach enables us to derive the higher order terms using only algebraic computation. Furthermore, this method enables us to derive not only the price of European options but also the price of options with an early exercise feature, such as Bermudan options and American options.

Keywords:

• Conditional characteristic function (CCF)
• asymptotic expansion
• CEV process
• Fourier analysis
• Bermudan options

2010 Mathematics Subject Classifications:

• 91G20
• 65T50
• 41A60

Acknowledgments

I thank an anonymous referees for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This paper was funded by Grant-in-Aid for Scientific Research (C) 16K03731, Japan Society for the Promotion of Science.