Dynamic Asymmetric Leverage in Stochastic Volatility Models

Soka University, Edo, Tokyo, Japan
Econometric Reviews (Impact Factor: 1.19). 07/2005; 24(3):317-332. DOI: 10.1080/07474930500243035
Source: RePEc


In the class of stochastic volatility (SV) models, leverage effects are typically specified through the direct correlation between the innovations in both returns and volatility, resulting in the dynamic leverage (DL) model. Recently, two asymmetric SV models based on threshold effects have been proposed in the literature. As such models consider only the sign of the previous return and neglect its magnitude, this paper proposes a dynamic asymmetric leverage (DAL) model that accommodates the direct correlation as well as the sign and magnitude of the threshold effects. A special case of the DAL model with zero direct correlation between the innovations is the asymmetric leverage (AL) model. The dynamic asymmetric leverage models are estimated by the Monte Carlo likelihood (MCL) method. Monte Carlo experiments are presented to examine the finite sample properties of the estimator. For a sample size of T = 2000 with 500 replications, the sample means, standard deviations, and root mean squared errors of the MCL estimators indicate only a small finite sample bias. The empirical estimates for S&P 500 and TOPIX financial returns, and USD/AUD and YEN/USD exchange rates, indicate that the DAL class, including the DL and AL models, is generally superior to threshold SV models with respect to AIC and BIC, with AL typically providing the best fit to the data.

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    • "where k is a parameter vector of length q k and explanatory variable vector v k,t is of length q k . This term is used in the S&P 500 analysis of Section 5.1 for modelling the leverage e↵ect using asymmetric stochastic volatility (see for example Asai and McAleer, 2005; Omori et al., 2007 "
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    • "The and parameters of the above model, capturing leverage and threshold e¤ects, respectively, can not be identi…ed, separately. That is, when E(" t t ) = 0 (implying = 0), this model can yield the same magnitude of leverage e¤ects to those implied by the SV model allowing for leverage e¤ects (see equation (4) of Asai and McAleer (2004)). This problem is not present in our model since Cov (" t ; I(A t ) t ) = E [ t ] Cov (" t ; I(A t )) = 0. sharply to large negative stock return shocks compared to large positive shocks of the same magnitude (see, e.g., Bekaert and Wu (2000), Kane et al (2000), Yu (2004) and Ederington and Guan (2010)). "
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    • "Nelson [18] and Glosten et al. [19] considered extensions to GARCH models, namely, the EGARCH model and the GJR-GARCH model, respectively, to incorporate the asymmetry in volatility. So et al. [20] and Asai and McAleer [21], [22] investigated extensions to SV models by incorporating asymmetry in volatility. So et al. [20] introduced a threshold autoregressive stochastic volatility (TARSV) model, which is regarded as the SV counterpart of the threshold ARCH model of Li and Li [23] 1 . "
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