Stochastic Volatility Filtering with Intractable Likelihoods

TL;DR

This paper introduces an auxiliary particle filter based on approximate Bayesian computation for stochastic volatility models with intractable likelihoods, particularly useful for financial data with heavy tails and asymmetry.

Contribution

It develops a novel ABC-APF that enhances state estimation in models with intractable likelihoods, improving accuracy and flexibility over existing methods.

Findings

The ABC-APF performs well on simulated data from alpha-stable models.

It outperforms existing ABC filters in accuracy.

The method is applicable to any hidden Markov model with intractable likelihoods.

Abstract

This paper is concerned with particle filtering for $\alpha$-stable stochastic volatility models. The $\alpha$-stable distribution provides a flexible framework for modeling asymmetry and heavy tails, which is useful when modeling financial returns. An issue with this distributional assumption is the lack of a closed form for the probability density function. To estimate the volatility of financial returns in this setting, we develop a novel auxiliary particle filter. The algorithm we develop can be easily applied to any hidden Markov model for which the likelihood function is intractable or computationally expensive. The approximate target distribution of our auxiliary filter is based on the idea of approximate Bayesian computation (ABC). ABC methods allow for inference on posterior quantities in situations when the likelihood of the underlying model is not available in closed form, but simulating samples from it is possible. The ABC auxiliary particle filter (ABC-APF) that we propose provides not only a good alternative to state estimation in stochastic volatility models, but it also improves on the existing ABC literature. It allows for more flexibility in state estimation while improving on the accuracy through better proposal distributions in cases when the optimal importance density of the filter is unavailable in closed form. We assess the performance of the ABC-APF on a simulated dataset from the $\alpha$-stable stochastic volatility model and compare it to other currently existing ABC filters.