A generalized Esscher transform for option valuation with regime switching risk

Abstract

A generalized Esscher transform is introduced for option valuation in a Markov regime-switching model. It is intended that the generalized Esscher transform might provide novel insights into pricing regime switching risk. A new pricing kernel and the related martingale condition are derived which might provide a convenient way to price both diffusion and regime switching risks. Numerical studies are provided to illustrate the proposed method.

Keywords:

• Option pricing
• Generalized Esscher transform
• Regime switching risk
• Martingale condition

JEL Classifications:

• G12
• G13

Acknowledgments

The authors would like to thank the two reviewers for their helpful and insightful comments. We would like to acknowledge support from the Discovery Grant from the Australian Research Council (ARC), (Project No.: DP190102674).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The discussions in this section are motivated by some comments from the two referees. We are grateful for their insightful comments.

Additional information

Funding

This work was supported by the Discovery Grant from the Australian Research Council (ARC) [DP190102674].