A hidden Markov regime-switching model for option valuation

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 (C) 2010 Elsevier B V All rights reserved