Gradient-based simulated maximum likelihood estimation for Lévy-driven Ornstein–Uhlenbeck stochastic volatility models |
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Authors: | Yi-Jie Peng Michael C Fu |
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Institution: | 1. Department of Management Science, School of Management, Fudan University, Shanghai, China.;2. The Robert H. Smith School of Business, Institute for Systems Research, University of Maryland, College Park, MD 20742-1815, USA. |
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Abstract: | This paper studies the parameter estimation problem for Ornstein–Uhlenbeck stochastic volatility models driven by Lévy processes. Estimation is regarded as the principal challenge in applying these models since they were proposed by Barndorff-Nielsen and Shephard J. R. Stat. Soc. Ser. B, 2001, 63(2), 167–241]. Most previous work has used a Bayesian paradigm, whereas we treat the problem in the framework of maximum likelihood estimation, applying gradient-based simulation optimization. A hidden Markov model is introduced to formulate the likelihood of observations; sequential Monte Carlo is applied to sample the hidden states from the posterior distribution; smooth perturbation analysis is used to deal with the discontinuities introduced by jumps in estimating the gradient. Numerical experiments indicate that the proposed gradient-based simulated maximum likelihood estimation approach provides an efficient alternative to current estimation methods. |
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Keywords: | Maximum likelihood OU processes Stochastic volatility Lévy processes Simulation optimization Sequential Monte Carlo |
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