Dynamic Asymmetric Leverage in Stochastic Volatility Models
ABSTRACT 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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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.Applied Mathematics and Computation. 01/2011; 218:61-75.
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ABSTRACT: Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility models with skewness driven by hidden Markov Chain with switching.09/2012;
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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%.04/2012;