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

Dong-Mei Zhu (), Jiejun Lu (), Wai-Ki Ching () and Tak Kuen Siu
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Dong-Mei Zhu: Southeast University
Jiejun Lu: The University of Hong Kong
Wai-Ki Ching: The University of Hong Kong

Computational Economics, 2019, vol. 53, issue 2, No 4, 555-586

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10614-017-9754-9

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