A triple-threshold leverage stochastic volatility model

Abstract

In this paper we introduce a triple-threshold leverage stochastic volatility (TTLSV) model for financial return time series. The main feature of the model is to allow asymmetries in the leverage effect as well as mean and volatility. In the model the asymmetric effect is modeled by a threshold nonlinear structure that the two regimes are determined by the sign of the past returns. The model parameters are estimated using maximum likelihood (ML) method based on the efficient importance sampling (EIS) technique. Monte Carlo simulations are presented to examine the accuracy and finite sample properties of the proposed methodology. The EIS-based ML (EIS-ML) method shows good performance according to the Monte Carlo results. The proposed model and methodology are applied to two stock market indices for China. Strong evidence of the mean and volatility asymmetries is detected in Chinese stock market. Moreover, asymmetries in the volatility persistence and leverage effect are also discovered. The log-likelihood and Akaike information criterion (AIC) suggest evidence in favor of the proposed model. In addition, model diagnostics suggest that the proposed model performs relatively well in capturing the key features of the data. Finally, we compare models in a Value at Risk (VaR) study. The results show that the proposed model can yield more accurate VaR estimates than the alternatives.

Threshold stochastic volatility: Properties and forecasting

“…Wang (2012) also compares the TSV model empirically with the asymmetric SV model proposed by Asai and McAleer (2005), in order to consider different distributions for standardized returns, and concludes that the A-ARSV model has a better fit. Finally, Wu and Zhou (2015) find very weak evidence in favour of a TSV specification.…”

“…E-mail address: ortega@est-econ.uc3m.es (E. Ruiz). Liu (2011), Elliott, Liew, andSiu (2011), Fan andWang (2013), Ghosh, Gurung, andSource (2015), Liu, Wong, An, and Zhang (2014), Montero-Lorenzo, Fernández-Avilés, and García-centeno (2010), Muñoz, Marquez, and Acosta (2007), Smith (2009), Choi (2008, 2009), Tsai-Hung and , Wu and Zhou (2015), Wirjanto, Kolkiewicz, and Men (2016), and Xu (2012). However, to the best of our knowledge, the statistical properties of TSV models are unknown, which makes it difficult to assess their advantages and limitations relative to alternative specifications of the leverage.…”

Integrated nested Laplace approximations for threshold stochastic volatility models

“…For more examples on the threshold stochastic volatility seeAsai and McAleer (2004,Chen et al (2008Chen et al ( , 2013,Elliott et al (2011), Ghosh et al (2015,Wu and Zhou (2015) andWirjanto et al (2016), among others.…”

Data cloning estimation for asymmetric stochastic volatility models

“…For more examples on the negative correlation between returns and future volatility seeYu (2005), and on the threshold stochastic volatility seeAsai and McAleer (2004, 2005, 2011,Chen et al (2008Chen et al ( , 2013,Elliott et al (2011), Ghosh et al (2015,Wu and Zhou (2015) andWirjanto et al (2016), among others.…”