Affiliations: Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, Hungary
Correspondence:
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Corresponding author: I. Róbert Sipos, Department of Networked Systems and Services, Budapest University of Technology and Economics, H-1117 Budapest, Magyar tudósok körútja 2, Hungary. E-mail: [email protected].
Abstract: In this paper we propose stochastic time series prediction by autoregressive Hidden Markov Models (AR-HMM). The model parameter estimation, hence the prediction, is carried out by Markov chain Monte Carlo (MCMC) sampling instead of finding a single maximum likelihood model. Estimating the whole distribution can provide us with more insight about the underlying stochastic process. As opposed to trading directly on a financial instrument, the predicted future distribution of the underlying asset is then used for option portfolio optimization, where we consider a portfolio of plain vanilla put and call European options with different strike prices. The optimization itself is carried out using linear programming with optional risk constraints. The nature of MCMC sampling of AR-HMMs exhibits algorithmic properties which make a massively parallel implementation feasible and beneficial. The models are implemented using Graphics Processing Units (GPU) to achieve superior performance. The performance of the novel methods has been extensively tested on real financial time series, such as SPY and USO, where they could secure a profit and outperformed the traditional maximum likelihood approaches.
