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Particle Gibbs for likelihood-free inference of stochastic volatility models

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Abstract

Stochastic volatility models (SVMs) are widely used in finance and econometrics for analyzing and interpreting volatility. Real financial data are often observed to have heavy tails, which violate a Gaussian assumption and may be better modeled using the stable distribution. However, the intractable density of the stable distribution hinders the use of common computational methods such as Markov chain Monte Carlo (MCMC) for parameter inference of SVMs. In this paper, we propose a new particle Gibbs sampler as a strategy to handle SVMs with intractable likelihoods in the approximate Bayesian computation (ABC) setting. The proposed sampler incorporates a conditional auxiliary particle filter, which can help mitigate the weight degeneracy often encountered when using ABC. Simulation studies demonstrate the efficacy of our sampler for inferring SVM parameters when compared to existing particle Gibbs samplers based on the conditional bootstrap filter, and for inferring both SVM and stable distribution parameters when compared to existing particle MCMC samplers. As a real data application, we apply the proposed sampler for fitting an SVM to S&P 500 Index time-series data during the 2008–2009 financial crisis.

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Acknowledgements

This work was partially supported by Discovery Grant RGPIN-2019-04771 from the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Waterloo, 200 University Ave W, Waterloo, ON, N2L 3G1, Canada

    Zhaoran Hou & Samuel W. K. Wong

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  1. Zhaoran Hou
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  2. Samuel W. K. Wong
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Correspondence to Samuel W. K. Wong.

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Hou, Z., Wong, S.W.K. Particle Gibbs for likelihood-free inference of stochastic volatility models. Stat Comput 35, 34 (2025). https://doi.org/10.1007/s11222-025-10571-4

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