A hidden Markov regime-switching model for option valuation

Chuin Ching Liew*, Tak Kuen Siu

*Corresponding author for this work

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We investigate two approaches, namely, the Esscher transform and the extended Girsanov's principle, for option valuation in a discrete-time hidden Markov regime-switching Gaussian model. The model's parameters including the interest rate, the appreciation rate and the volatility of a risky asset are governed by a discrete-time, finite-state, hidden Markov chain whose states represent the hidden states of an economy. We give a recursive filter for the hidden Markov chain and estimates of model parameters using a filter-based EM algorithm. We also derive predictors for the hidden Markov chain and some related quantities. These quantities are used to estimate the price of a standard European call option. Numerical examples based on real financial data are provided to illustrate the implementation of the proposed method.

Original languageEnglish
Pages (from-to)374-384
Number of pages11
JournalInsurance: Mathematics and Economics
Volume47
Issue number3
DOIs
Publication statusPublished - Dec 2010

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