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.
"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 "
[Show abstract][Hide abstract] ABSTRACT: In many settings of empirical interest, time variation in the distribution parameters is important for capturing the dynamic behaviour of time series processes. Although the fitting of heavy tail distributions has become easier due to computational advances, the joint and explicit modelling of time-varying conditional skewness and kurtosis is a challenging task. We propose a class of parameter-driven time series models referred to as the generalized structural time series (GEST) model. The GEST model extends Gaussian structural time series models by a) allowing the distribution of the dependent variable to come from any parametric distribution, including highly skewed and kurtotic distributions (and mixed distributions) and b) expanding the systematic part of parameter-driven time series models to allow the joint and explicit modelling of all the distribution parameters as structural terms and (smoothed) functions of independent variables. The paper makes an applied contribution in the development of a fast local estimation algorithm for the evaluation of a penalised likelihood function to update the distribution parameters over time without the need for evaluation of a high-dimensional integral based on simulation methods.
"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)). "
[Show abstract][Hide abstract] ABSTRACT: This paper presents a new stochastic volatility model which allows for persistent shifts in volatility of stock market returns, referred to as structural breaks. These shifts are endogenously driven by large return shocks (innovations), reflecting large pieces of market news. These shocks are identified from the data as being bigger than the values of two threshold parameters of the model: one for the negative shocks and one for the positive shocks. The model can be employed to investigate economic (or market) sources of volatility shifts, without relying on exogenous information from the sample. In addition to this, it has a number of interesting features which enables us to study the dynamic or changing in magnitude effects of large return shocks on future levels of market volatility. The above properties of the model are shown based on a study for the US stock market volatility. For this market, the model identifies from the data as large negative return shocks these which are smaller than -2.05% on weekly basis, while as large positive return shocks those which are bigger than 2.33%.
"Nelson  and Glosten et al.  considered extensions to GARCH models, namely, the EGARCH model and the GJR-GARCH model, respectively, to incorporate the asymmetry in volatility. So et al.  and Asai and McAleer ,  investigated extensions to SV models by incorporating asymmetry in volatility. So et al.  introduced a threshold autoregressive stochastic volatility (TARSV) model, which is regarded as the SV counterpart of the threshold ARCH model of Li and Li  1 . "
[Show abstract][Hide abstract] ABSTRACT: We derive a nonlinear filter and the corresponding filter-based estimates for a threshold autoregressive stochastic volatility (TARSV) model. Using the technique of a reference probability measure, we derive a nonlinear filter for the hidden volatility and related quantities. The filter-based estimates for the unknown parameters are then obtained from the EM algorithm.
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