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IMA Journal of Management Mathematics Advance Access published online on June 11, 2009
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpp009
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© The authors 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Hidden Markov models for financial optimization problems

Diana Roman{dagger} and Gautam Mitra{ddagger}

Centre for the Analysis of Risk and Optimisation Modelling Applications, School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex UB8 3PH, UK and Optirisk Systems, Uxbridge, Middlesex UB9 4DA, UK

Nicola Spagnolo§

Department of Economics and Finance, School of Social Sciences, Brunel University, Uxbridge, Middlesex, UB8 3PH UK and Centre for Applied Macroeconomic Analysis, Canberra, Australia

{dagger} Corresponding author. Email: diana.roman{at}brunel.ac.uk

{ddagger} Email: gautam.mitra{at}brunel.ac.uk

§ Email: nicola.spagnolo{at}brunel.ac.uk

Received on 2 July 2007. Accepted on 14 July 2008.

Many financial decision problems require scenarios for multivariate financial time series that capture their sequentially changing behaviour, including their extreme movements. We consider modelling financial time series by hidden Markov models (HMMs), which are regime-switching-type models. Estimating the parameters of an HMM is a difficult task and the multivariate case can pose serious implementation issues. After the parameter estimation, the calibrated model can be used as a scenario generator to describe the future realizations of asset prices. The scenario generator is tested in a single-period mean–conditional value-at-risk optimization problem for portfolio selection.

Keywords: scenario generation; asset pricing; hidden Markov models; extreme events; stability; conditional value at risk


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