339 research outputs found

    A multivariate generalized independent factor GARCH model with an application to financial stock returns

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    We propose a new multivariate factor GARCH model, the GICA-GARCH model , where the data are assumed to be generated by a set of independent components (ICs). This model applies independent component analysis (ICA) to search the conditionally heteroskedastic latent factors. We will use two ICA approaches to estimate the ICs. The first one estimates the components maximizing their non-gaussianity, and the second one exploits the temporal structure of the data. After estimating the ICs, we fit an univariate GARCH model to the volatility of each IC. Thus, the GICA-GARCH reduces the complexity to estimate a multivariate GARCH model by transforming it into a small number of univariate volatility models. We report some simulation experiments to show the ability of ICA to discover leading factors in a multivariate vector of financial data. An empirical application to the Madrid stock market will be presented, where we compare the forecasting accuracy of the GICA-GARCH model versus the orthogonal GARCH one

    A multivariate generalized independent factor GARCH model with an application to financial stock returns

    Get PDF
    We propose a new multivariate factor GARCH model, the GICA-GARCH model , where the data are assumed to be generated by a set of independent components (ICs). This model applies independent component analysis (ICA) to search the conditionally heteroskedastic latent factors. We will use two ICA approaches to estimate the ICs. The first one estimates the components maximizing their non-gaussianity, and the second one exploits the temporal structure of the data. After estimating the ICs, we fit an univariate GARCH model to the volatility of each IC. Thus, the GICA-GARCH reduces the complexity to estimate a multivariate GARCH model by transforming it into a small number of univariate volatility models. We report some simulation experiments to show the ability of ICA to discover leading factors in a multivariate vector of financial data. An empirical application to the Madrid stock market will be presented, where we compare the forecasting accuracy of the GICA-GARCH model versus the orthogonal GARCH one.ICA, Multivariate GARCH, Factor models, Forecasting volatility

    An ICA-GARCH approach to computing portfolio VAR with applications to South African financial markets

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    Master of Management in Finance & Investment Faculty of Commerce Law and Management Wits Business School University of The Witwatersrand 2016The Value-at-Risk (VaR) measurement – which is a single summary, distribution independent statistical measure of losses arising as a result of market movements – has become the market standard for measuring downside risk. There are some diverse ways to computing VaR and with this diversity comes the problem of determining which methods accurately measure and forecast Value-at-Risk. The problem is two-fold. First, what is the distribution of returns for the underlying asset? When dealing with linear financial instruments – where the relationship between the return on the financial asset and the return on the underlying is linear– we can assume normality of returns. This assumption becomes problematic for non-linear financial instruments such as options. Secondly, there are different methods of measuring the volatility of the underlying asset. These range from the univariate GARCH to the multivariate GARCH models. Recent studies have introduced the Independent Component Analysis (ICA) GARCH methodology which is aimed at computational efficiency for the multivariate GARCH methodologies. In our study, we focus on non-linear financial instruments and contribute to the body of knowledge by determining the optimal combination for the measure for volatility of the underlying (univariate-GARCH, EWMA, ICA-GARCH) and the distributional assumption of returns for the financial instrument (assumption of normality, the Johnson translation system). We use back-testing and out-of-sample tests to validate the performance of each of these combinations which give rise to six different methods for value-at-risk computations.MT201

    Multivariate GARCH estimation via a Bregman-proximal trust-region method

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    The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parameters are subjected to convoluted nonlinear constraints necessary to ensure, for instance, the existence of stationary solutions and the positive semidefinite character of the conditional covariance matrices used in the model design. So far, this problem has been addressed in the literature only in low dimensional cases with strong parsimony constraints. In this paper we propose a general formulation of the estimation problem in any dimension and develop a Bregman-proximal trust-region method for its solution. The Bregman-proximal approach allows us to handle the constraints in a very efficient and natural way by staying in the primal space and the Trust-Region mechanism stabilizes and speeds up the scheme. Preliminary computational experiments are presented and confirm the very good performances of the proposed approach.Comment: 35 pages, 5 figure

    GHICA - Risk Analysis with GH Distributions and Independent Components

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    Over recent years, study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical difficulty. The primary aim of this paper is to present a realistic and fast method, GHICA, which overcomes the limitations in multivariate risk analysis. The idea is to first retrieve independent components (ICs) out of the observed high-dimensional time series and then individually and adaptively fit the resulting ICs in the generalized hyperbolic (GH) distributional framework. For the volatility estimation of each IC, the local exponential smoothing technique is used to achieve the best possible accuracy of estimation. Finally, the fast Fourier transformation technique is used to approximate the density of the portfolio returns. The proposed GHICA method is applicable to covariance estimation as well. It is compared with the dynamic conditional correlation (DCC) method based on the simulated data with d = 50 GH distributed components. We further implement the GHICA method to calculate risk measures given 20-dimensional German DAX portfolios and a dynamic exchange rate portfolio. Several alternative methods are considered as well to compare the accuracy of calculation with the GHICA one.Multivariate Risk Management, Independent Component Analysis, Generalized Hyperbolic Distribution, Local Exponential Estimation, Value at Risk, Expected Shortfall.

    The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey

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    This paper provides a selected review of the recent developments and applications of mixtures of normal (MN) distribution models in empirical finance. Once attractive property of the MN model is that it is flexible enough to accommodate various shapes of continuous distributions, and able to capture leptokurtic, skewed and multimodal characteristics of financial time series data. In addition, the MN-based analysis fits well with the related regime-switching literature. The survey is conducted under two broad themes: (1) minimum-distance estimation methods, and (2) financial modeling and its applications.Mixtures of Normal, Maximum Likelihood, Moment Generating Function, Characteristic Function, Switching Regression Model, (G) ARCH Model, Stochastic Volatility Model, Autoregressive Conditional Duration Model, Stochastic Duration Model, Value at Risk.
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