Bayesian Analysis

Filtering and Estimation for a Class of Stochastic Volatility Models with Intractable Likelihoods

Emilian R. Vankov, Michele Guindani, and Katherine B. Ensor

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Abstract

We introduce a new approach to latent state filtering and parameter estimation for a class of stochastic volatility models (SVMs) for which the likelihood function is unknown. The α-stable stochastic volatility model provides a flexible framework for capturing asymmetry and heavy tails, which is useful when modeling financial returns. However, the α-stable distribution lacks a closed form for the probability density function, which prevents the direct application of standard Bayesian filtering and estimation techniques such as sequential Monte Carlo and Markov chain Monte Carlo. To obtain filtered volatility estimates, we develop a novel approximate Bayesian computation (ABC) based auxiliary particle filter, which provides improved performance through better proposal distributions. Further, we propose a new particle based MCMC (PMCMC) method for joint estimation of the parameters and latent volatility states. With respect to other extensions of PMCMC, we introduce an efficient single filter particle Metropolis-within-Gibbs algorithm which can be applied for obtaining inference on the parameters of an asymmetric α-stable stochastic volatility model. We show the increased efficiency in the estimation process through a simulation study. Finally, we highlight the necessity for modeling asymmetric α-stable SVMs through an application to propane weekly spot prices.

Article information

Source
Bayesian Anal., Volume 14, Number 1 (2019), 29-52.

Dates
First available in Project Euclid: 28 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.ba/1522202635

Digital Object Identifier
doi:10.1214/18-BA1099

Keywords
particle Markov chain Monte Carlo auxiliary particle filter approximate Bayesian computation stable distribution

Rights
Creative Commons Attribution 4.0 International License.

Citation

Vankov, Emilian R.; Guindani, Michele; Ensor, Katherine B. Filtering and Estimation for a Class of Stochastic Volatility Models with Intractable Likelihoods. Bayesian Anal. 14 (2019), no. 1, 29--52. doi:10.1214/18-BA1099. https://projecteuclid.org/euclid.ba/1522202635


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