A tree approach to options pricing under regime-switching jump diffusion models

Abstract

A simple, efficient tree is developed to price options in a very general regime-switching jump diffusion model. Under this model, the switching rates of the switching process depend on the underlying stock price process. Sufficient conditions that guarantee the positivity of branch probabilities are provided. Using the regime-switching tree, we approximate Heston's stochastic volatility model with an additional jump component. Finally, we illustrate the effectiveness of the tree method by several numerical examples.

Keywords:

• option pricing
• regime-switching model
• trinomial tree
• stochastic approximation
• financial derivatives

2010 AMS Subject Classifications:

• 91G80
• 93E11
• 93E20

Acknowledgments

We are grateful to the two anonymous referees and the editor for their valuable comments, which helped to improve the exposition of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.