Asymmetry in stochastic volatility models with threshold and time-dependent correlation

Torben Schäfers; Long Teng

doi:10.1515/snde-2021-0020

Abstract

In this work we study the effects by including threshold, constant and time-dependent correlation in stochastic volatility (SV) models to capture the asymmetry relationship between stock returns and volatility. We develop SV models which include only time-dependent correlated innovations and both threshold and time-dependent correlation, respectively. It has been shown in literature that the SV model with only constant correlation does a better job of capturing asymmetry than threshold stochastic volatility (TSV) model. We show here that the SV model with time-dependent correlation performs better than the model with constant correlation on capturing asymmetry, and the comprehensive model with both threshold and time-dependently correlated innovations dominates models with pure threshold, constant and time-dependent correlation, and both threshold and constant correlation as well. In our comprehensive model, volatility and returns are time-dependently correlated, where the time-varying correlation is negative, and the volatility is more persistent, less volatile and higher following negative returns as expected. An empirical study is provided to illustrate our findings.

Keywords: asymmetry volatility; stochastic volatility model; threshold; time-dependent correlation

Corresponding author: Long Teng, Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119, Wuppertal, Germany, E-mail: teng@math.uni-wuppertal.de

Acknowledgments

The work of authors was partially supported by the bilateral German-Hong Kong Project ADDRESS - Asymmetry in Dynamically Correlated Threshold Stochastic Volatility Model, financed by the DAAD and the University Grants Committee (UGC) of Hong Kong. The authors appreciate the anonymous referee’s valuable and profound comments.

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2021-0020).

Received: 2021-02-15

Revised: 2022-03-11

Accepted: 2022-03-17

Published Online: 2022-04-13

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