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9. Two-Time-Scale Switching Diffusions

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Authors
Hai-Dang Nguyen
George Yin
Chao Zhu
Published in
Hybrid Switching Diffusions
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the intricate world of two-time-scale switching diffusions, focusing on their application in option pricing and the modeling of stochastic volatility. The text begins by introducing the concept of regime-switching diffusions and their role in capturing the dynamic nature of stock prices and other derivatives. It then explores the use of asymptotic expansions to develop a deeper understanding of option pricing under these diffusions. The chapter also examines the ergodicity of switching diffusions, particularly when the states of the discrete event process belong to several weakly connected ergodic classes. The text provides a detailed analysis of the positive recurrence and ergodicity of these systems, using techniques such as singular perturbation methods and perturbed Lyapunov function methods. The chapter concludes with a discussion on the implications of these findings for the modeling and analysis of complex systems. Readers will gain a comprehensive understanding of the behavior of switching diffusions and their applications in financial mathematics, as well as insights into the latest research in this field.
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previous chapter Invariance Principles
next chapter Switching Jump Diffusions: Time-Scale Separations
Title
Two-Time-Scale Switching Diffusions
Authors
Hai-Dang Nguyen
George Yin
Chao Zhu
Copyright Year
2025
Book
Hybrid Switching Diffusions

Print ISBN: 978-3-031-93302-8

Electronic ISBN: 978-3-031-93303-5

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-031-93303-5_9
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