A New Approach to Volatility Modeling: The Factorial Hidden Markov Volatility Model

Abstract

A new process—the factorial hidden Markov volatility (FHMV) model—is proposed to model financial returns or realized variances. Its dynamics are driven by a latent volatility process specified as a product of three components: a Markov chain controlling volatility persistence, an independent discrete process capable of generating jumps in the volatility, and a predictable (data-driven) process capturing the leverage effect. An economic interpretation is attached to each one of these components. Moreover, the Markov chain and jump components allow volatility to switch abruptly between thousands of states, and the transition matrix of the model is structured to generate a high degree of volatility persistence. An empirical study on six financial time series shows that the FHMV process compares favorably to state-of-the-art volatility models in terms of in-sample fit and out-of-sample forecasting performance over time horizons ranging from 1 to 100 days. Supplementary materials for this article are available online.

KEY WORDS:

• Hierarchical hidden Markov model
• Leverage effect
• Markov-switching
• Persistence
• Volatility.

SUPPLEMENTARY MATERIALS

The supplementary materials include a MATLAB program for estimating the FHMV model and an online appendix. Section 1 of this appendix provides a discussion of hierarchical and factorial hidden Markov models in the context of volatility modeling, with some economic interpretations. Section 2 contains the proofs of Theorem 1 and Propositions 1 and 2 of the article. Section 3 discusses some computational aspects associated with the estimation of the FHMV model. Sections 4 and 5 describe, respectively, the competing return and realized variance models used in the empirical study.

ACKNOWLEDGMENTS

Maciej Augustyniak acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada. Arnaud Dufays acknowledges financial support from the Fonds de recherche du Québec – Société et culture and from the Social Sciences and Humanities Research Council of Canada via the project 430-2017-00215. The authors are grateful to three anonymous referees for providing valuable comments on an earlier draft as well as to seminar participants at University of Namur and to 2017 SoFiE conference participants at the NYU Stern School of Business (in particular to Eric Ghysels who was the article’s discussant).