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Volume 15,     Number 1,     Spring 2007

 

A HIDDEN MARKOV MULTI-ASSETS
PRICE MODEL
ROBERT J. ELLIOTT, TAO LIN AND HONG MIAO

Abstract. Prices for some real world tradable assets, for instance natural gas and oil, are correlated, and the price dynamics for those assets are different in different economic environments. In this paper we extend the mean reverting model to multi-assets and model correlation between prices. Our model also allows the means and the mean reverting factors to switch between different regimes by including a Hidden Markov chain which models the different economic environments, or "states of the world." We then obtain approximate estimates for the parameters by applying filters and the EM algorithm. Approximate derivative prices are also given.

 

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