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Nonlinearity and Endogeneity in Continuous-Time Regime-Switching Diffusion Models for Market Volatility

Bu, Ruijun; Cheng, Jie; Hadri, Kaddour


Ruijun Bu

Kaddour Hadri


We examine model specification in regime-switching continuous-time diffusions for modeling S&P 500 Volatility Index (VIX). Our investigation is carried out under two nonlinear diffusion frameworks, the NLDCEV and the CIRCEV frameworks, and our focus is on the nonlinearity in regime-dependent drift and diffusion terms, the switching components, and the endogeneity in regime changes. While we find strong evidence of regime-switching effects, models with a switching diffusion term capture the VIX dynamics considerably better than models with only a switching drift, confirming the presence and importance of volatility regimes. Strong evidence of nonlinear endogeneity in regime changes is also detected. Meanwhile, we find significant nonlinearity in the regime-dependent diffusion specification, suggesting that the nonlinearity in the VIX dynamics cannot be accounted for by regime-switching effects alone. Finally, we find that models based on the CIRCEV specification are significantly closer to the true data generating process of VIX than models based on the NLDCEV specification uniformly across all regime-switching specifications.

Journal Article Type Article
Acceptance Date Jul 2, 2016
Publication Date Jul 2, 2016
Journal Studies in Nonlinear Dynamics and Econometrics
Publisher De Gruyter
Peer Reviewed Peer Reviewed
Volume 21
Issue 1
Keywords constant elasticity volatility; endogeneity; maximum likelihood estimation; nonlinear diffusion; regime-switching model; volatility index
Publisher URL