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

Author

Listed:
  • Dong-Mei Zhu

    (Southeast University)

  • Jiejun Lu

    (The University of Hong Kong)

  • Wai-Ki Ching

    (The University of Hong Kong
    Hughes Hall
    Beijing University of Chemical Technology)

  • Tak-Kuen Siu

    (Macquarie University)

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.

Suggested Citation

  • Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    • Handle: RePEc:kap:compec:v:53:y:2019:i:2:d:10.1007_s10614-017-9754-9
    DOI: 10.1007/s10614-017-9754-9
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