Non-Gaussian Stochastic Volatility Model Research Articles

Non-Gaussian stochastic volatility model with jumps via Gibbs sampler

Compreender o comportamento dos ativos financeiros e de extrema importância para determinar a alocacao de capital entre as diferentes formas de investimento disponiveis. Tal escolha depende, dentre outros fatores, da percepcao do individuo acerca dos riscos e retornos associados a essas opcoes de investimentos. Na literatura, encontram-se diversos modelos cujo objetivo e estimar o risco de aplicacoes financeiras, entretanto, a maioria depende de metodos MCMC baseados em algoritmos Metropolis, o que os torna computacionalmente custosos. O presente trabalho apresenta um modelo alternativo, o Modelo Na?o Gassiano de Volatilidade Estocastica Com Saltos (NGSVJ), baseado nos Modelos Dinâmicos Lineares (DLM) com mistura, capaz de estimar a volatilidade sem recorrer a metodos computacionais intensivos, utilizando apenas o Amostrador de Gibbs. Isso e possivel devido a estrutura do modelo, que permite obter as condicionais completas a posteriori para os parâmetros. Alem disso, a insercao de saltos nos retornos no modelo o permite capturar os movimentos especulativos pontuais do mercado, sem que isso se traduza em aumento da volatilidade. Sao apresentados estudos de simulacao a fim de investigar a eficacia do metodo proposto e, ao final, realiza-se uma analise com dados reais de retornos dos indices S&P 500 e iBovespa. Os resultados indicam que o modelo proposto foi capaz de estimar a volatilidade, com resultados semelhantes aos de outros modelos existentes na literatura, de forma computacionalmente eficaz e automatizada, sendo que sua capacidade de identificar saltos e maior quando a serie de retornos em estudo possui movimentos especulativos fortes. Um metodo nao parametrico tambem foi utilizado para estimar os saltos, mas os resultados de simulacao mostraram que ele nao foi eficaz..

Modeling volatility dynamics using non-Gaussian stochastic volatility model based on band matrix routine

Substantial evidence supports that financial returns time series exhibit abnormal properties including leptokurtosis, volatility clustering as well as intermittent jumps and leverage effects between returns and volatility processes. This paper studies a heavy-tailed stochastic volatility (SV) model with jumps components and leverage effects, and the Student's-t distribution is employed to describe the error innovations (SVJLt). Since the existence of high-dimensionality of the latent variables and the special structure of Hessian matrix of the stochastic volatility density, we develop an efficient Markov chain Monte Carlo (MCMC) posterior simulator exploiting the adaptive importance sampling technique based on band and sparse matrix routine rather than the conventional Kalman filter to estimate the new model. And the precision sampler is exploited due to the band structure of the inverse covariance matrix of the state variables. The model comparisons of returns volatility are conducted utilizing the observed-data based deviance information criterion (DIC) and the cross-entropy (CE) based marginal likelihood estimation. The effectiveness of the proposed model and the methodology are illustrated with applications in stock returns volatility forecast. Through employing several loss functions for evaluation, the empirical studies suggest strong evidence in heavy tailed distributions, jumps features and leverage effects simultaneously.

Artifact Removal from Single-Trial ERPs using Non-Gaussian Stochastic Volatility Models and Particle Filter

This paper considers improved modeling of artifactual noise for denoising of single-trial event-related potentials (ERPs) by state-space approach. Instead of the inadequate constant variance models used in existing studies, we propose to use stochastic volatility (SV) models to better describe the time-varying volatility in real ERP noise sources. We further propose a class of non-Gaussian SV models to capture the abrupt volatility changes typically present in impulsive noise, to improve artifact removal from ERPs. Two specifications are considered: (1) volatility driven by a heavy-tailed component and (2) transformation of volatility. Both result in volatility processes with heavy-tailed transition densities which can predict the impulsive noise volatility dynamics, more accurately than the Gaussian models. These SV noise models are incorporated in an autoregressive (AR) state-space ERP dynamic model. Parameter estimation is done using a Rao-Blackwellized particle filter (RBPF). Evaluation on simulated auditory brainstem responses (ABRs), corrupted by real eye-blink artifacts, shows that the non-Gaussian models can accurately detect the artifact-induced abrupt volatility spikes, and able to uncover the underlying inter-trial dynamics. Among them, the log-SV model performs the best. The results on real data demonstrate significant artifact suppression.

Bayesian Estimation of Non-Gaussian Stochastic Volatility Models

In this paper, a general Non-Gaussian Stochastic Volatility model is proposed instead of the usual Gaussian model largely studied. We consider a new specification of SV model where the innovations of the return process have centered non-Gaussian error distribution rather than the standard Gaussian distribution usually employed. The model describes the behaviour of random time fluctuations in stock prices observed in the financial markets. It offers a response to better model the heavy tails and the abrupt changes observed in financial time series. We consider the Laplace density as a special case of non-Gaussian SV models to be applied to our data base. Markov Chain Monte Carlo technique, based on the bayesian analysis, has been employed to estimate the model’s parameters.

Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets

In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.

Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets

In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.

THE STOCHASTIC VOLATILITY MODEL OF BARNDORFF-NIELSEN AND SHEPHARD IN COMMODITY MARKETS

We consider the non-Gaussian stochastic volatility model of Barndorff-Nielsen and Shephard for the exponential mean-reversion model of Schwartz proposed for commodity spot prices. We analyze the properties of the stochastic dynamics, and show in particular that the log-spot prices possess a stationary distribution defined as a normal variance-mixture model. Furthermore, the stochastic volatility model allows for explicit forward prices, which may produce a hump structure inherited from the mean-reversion of the stochastic volatility. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process. We compare with the popular Heston stochastic volatility dynamics, and show that the Barndorff-Nielsen and Shephard model provides a more flexible framework in describing commodity spot prices. An empirical example on UK spot data is included.

A Multivariate Non-Gaussian Stochastic Volatility Model with Leverage for Energy Markets

Spot prices in energy markets exhibit special features like price spikes, mean-reversion inverse, stochastic volatility, inverse leverage effect and co-integration between the different commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. Second order structure and stationary issues of the model are analysed. Moreover the implied multivariate forward model is derived. Due to the flexibility of the model stylized facts of the forward curve as contango, backwardation and humps are explained. Moreover, a transformed-based method to price options on the forward is described, where fast and precise algorithms for price computations can be implemented. A simulation method for Monte Carlo generation of price paths is introduced.

Recursive estimation for continuous time stochastic volatility models

Volatility plays an important role in portfolio management and option pricing. Recently, there has been a growing interest in modeling volatility of the observed process by nonlinear stochastic process [S.J. Taylor, Asset Price Dynamics, Volatility, and Prediction, Princeton University Press, 2005; H. Kawakatsu, Specification and estimation of discrete time quadratic stochastic volatility models, Journal of Empirical Finance 14 (2007) 424–442]. In [H. Gong, A. Thavaneswaran, J. Singh, Filtering for some time series models by using transformation, Math Scientist 33 (2008) 141–147], we have studied the recursive estimates for discrete time stochastic volatility models driven by normal errors. In this paper, we study the recursive estimates for various classes of continuous time nonlinear non-Gaussian stochastic volatility models used for option pricing in finance.

Bayesian Inference for Nonlinear and Non-Gaussian Stochastic Volatility Model with Leverage Effect

Stochastic volatility (SV) models provide useful tools to describe the evolution of asset returns, which exhibit time-varying volatility. This paper extends a basic SV model to capture a leverage effect, a fat-tailed distribution of asset returns and a nonlinear relationship between the current volatility and the previous volatility process. The Bayesian approach with the Markov chain Monte Carlo method is employed to estimate model parameters. To assess the goodness of the estimated model, we calculated several Bayesian model selection criteria that include the Bayes factor, the Bayesian predictive information criterion and the deviance information criterion. The proposed method is tested on simulated data and then applied to daily returns on the Nikkei 225 index where several SV models are formally compared.

Non-Gaussian Filter and Smoother Based on the Pearson Distribution System

The Pearson distribution system can represent wide class of distributions with various skewness and kurtosis. We develop a practical approach of using all types of its distribution system including the type-IV distribution which was difficult to implement. We propose an easily implemented algorithm which uses less-memory and performs at a higher speed than other typical methods: using analytic approximation of successive conditional probability density functions for prediction and filtering by the Pearson distribution system in the case of both the system and observation noise being one-dimensional. By using the approximated probability density function and the numerical integration, we obtain mean, variance, skewness and kurtosis of the next distribution. We decide the next approximated distribution from the Pearson distribution system. We adopt these steps for the prediction, filtering and smoothing recursively. Our framework makes it possible to construct time series models with various noise distributions. We apply our non-Gaussian filter to the estimation of non-Gaussian stochastic volatility models of the stock returns. We compare our method with the typical method.

A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models

A maximum likelihood approach for the analysis of stochastic volatility models is developed. The method uses a recursive numerical integration procedure that directly calculates the marginal likelihood. Only conventional integration techniques are used, making this approach both flexible and simple. Experimentation shows that the method matches the performance of the best estimation tools currently in use. New stochastic volatility models are introduced and estimated. The model that best fits recent stock-index data is characterized by a highly non-Gaussian stochastic volatility innovation distribution. This model dominates a model that includes an autoregressive conditional heteroscedastic effect in the stochastic volatility process and a model that includes a stochastic volatility effect in the conditional mean.

A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models

A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models

A non-Gaussian stochastic volatility model

A non-Gaussian stochastic volatility model is proposed in this paper. The model assumes that the time series is distributed as a Pearson type-VII distribution. The scale parameter of the distribution, which corresponds to the volatility of the process, is stochastic and is described by an autoregressive model with a constant term. Since the Pearson type-VII distribution can represent a broad class of distributions, including the normal distribution and t-distribution, the proposed model can be considered as a natural extension of the ordinary stochastic volatility model. For estimating the parameters of the stochastic volatility model, we apply a non-Gaussian filter. The model can be further generalized to the case where the shape parameter of the Pearson type-VII distribution is also time-varying. The usefulness of the model is demonstrated by the analysis of stock-return data, which suggests the relevance of the model to managing financial market risk.