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Computational Economics

, Volume 53, Issue 2, pp 555–586 | Cite as

Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching

  • Dong-Mei Zhu
  • Jiejun Lu
  • Wai-Ki ChingEmail author
  • Tak-Kuen Siu
Article
  • 163 Downloads

Abstract

In this paper we discuss an option pricing problem in a hidden Markovian regime-switching model with a stochastic interest rate and volatility. Regime switches are attributed to structural changes in an hidden economic environment and are described by a continuous-time, finite-state, unobservable Markov chain. The model is then applied to the valuation of a standard European option. By means of the standard separation principle, filtering and option valuation problems are separated. Robust filters for the hidden states of the economy and their robust filtered estimates of unknown parameters from the expectation maximization algorithm are presented based on standard techniques in filtering theory. Then an explicit expression of a conditional characteristic function relevant to option pricing is presented and the valuation of the option is discussed using the inverse Fourier transformation approach. Using the limiting behavior of the conditional characteristic function, an efficient implementation of the transform inversion integral is considered. Numerical experiments are given to illustrate the flexibility of filtering algorithms and the significance of regime-switching in option pricing.

Keywords

Option pricing Hidden Markov model (HMM) Regime-switching Characteristic function Fourier transformation 

Notes

Acknowledgements

A two-page abstract of the paper has been accepted for presentation in 2016 International Congress on Banking, Economics, Finance, and Business, 24–26 June 2016, Sapporo, Japan. This research work was supported by Research Grants Council of Hong Kong under Grant Number 17301214, HKU Strategic Theme on Computation and Information and National Natural Science Foundation of China under Grant Number 71601044.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Dong-Mei Zhu
    • 1
  • Jiejun Lu
    • 2
  • Wai-Ki Ching
    • 2
    • 3
    • 4
    Email author
  • Tak-Kuen Siu
    • 5
  1. 1.School of Management and EconomicsSoutheast UniversityNanjingChina
  2. 2.Advanced Modeling and Applied Computing Laboratory, Department of MathematicsThe University of Hong KongPokfulamHong Kong
  3. 3.Hughes HallCambridgeUK
  4. 4.School of Economics and ManagementBeijing University of Chemical TechnologyBeijingChina
  5. 5.Department of Applied Finance and Actuarial Studies, Faculty of Business and EconomicsMacquarie UniversitySydneyAustralia

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