An asymptotic expansion for local-stochastic volatility with jump models

Abstract

This paper develops an asymptotic expansion method for general stochastic differential equations with jumps and their functions. By applying the method, we derive an explicit approximation formula for pricing options on functions of multiple assets under local-stochastic volatility with jump models. Moreover, we present numerical examples for pricing basket options based on the parameters calibrated to the actual market data, which confirms the validity of our method in practice.

Keywords:

• Asymptotic expansion
• local volatility
• stochastic volatility
• jump-diffusion

Acknowledgements

We are very grateful to the editors and an anonymous referee for their precious comments, which have improved the previous version of our paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by JSPS KAKENHI [grant number 25380389].