Download or read book Multivariate stochastic volatility via Wishart processes a continuation written by Wolfgang Rinnergschwentner and published by . This book was released on 2011 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multivariate Stochastic Volatility Via Wishart Random Processes written by Alexander Philipov and published by . This book was released on 2004 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial models for asset and derivatives pricing, risk management, portfolio optimization, and asset allocation rely on volatility forecasts. Time-varying volatility models, such as GARCH and Stochastic Volatility (SVOL), have been successful in improving forecasts over constant volatility models. We develop a new multivariate SVOL framework for modeling financial data that assumes covariance matrices stochastically varying through a Wishart process. In our formulation, scalar variances naturally extend to covariance matrices rather than vectors of variances as in traditional SVOL models. Model fitting is performed using Markov chain Monte Carlo simulation from the posterior distribution. Due to the complexity of the model, an efficiently designed Gibbs sampler is described that produces inferences with a manageable amount of computation. Our approach is illustrated on a multivariate time series of monthly industry portfolio returns. In a test of the economic value of our model, minimum-variance portfolios based on our SVOL covariance forecasts outperform out-of-sample portfolios based on alternative covariance models such as Dynamic Conditional Correlations and factor-based covariances.
Download or read book Essays on Multivariate Stochastic Volatility Models Using Wishart Processes written by Yu-Cheng Ku and published by . This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Matrix State Particle Filter for Wishart Stochastic Volatility Processes written by Roberto Casarin and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work deals with multivariate stochastic volatility models, which account for a time-varying variance-covariance structure of the observable variables. We focus on a special class of models recently proposed in the literature and assume that the covariance matrix is a latent variable which follows an autoregressive Wishart process. We review two alternative stochastic representations of the Wishart process and propose Markov-Switching Wishart processes to capture different regimes in the volatility level. We apply a full Bayesian inference approach, which relies upon Sequential Monte Carlo (SMC) for matrix-valued distributions and allows us to sequentially estimate both the parameters and the latent variables.
Download or read book Multivariate Continuous Time Stochastic Volatility Models Driven by a L vy Process written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Several multivariate stochastic models in continuous time are introduced and their probabilistic and statistical properties are studied in detail. All models are driven by Lévy processes and can generally be used to model multidimensional time series of observations. In this thesis the focus is on various stochastic volatility models for financial data. Firstly, multidimensional continuous-time autoregressive moving-average (CARMA) processes are considered and, based upon them, a multivariate continuous-time exponential GARCH model (ECOGARCH). Thereafter, positive semi-definite Ornstein-Uhlenbeck type processes are introduced and the behaviour of the square root (and similar transformations) of stochastic processes of finite variation, which take values in the positive semi-definite matrices and can be represented as the sum of an integral with respect to time and another integral with respect to an extended Poisson random measure, is analysed in general. The positive semi-definite Ornstein-Uhlenbeck type processes form the basis for the definition of a multivariate extension of the popular stochastic volatility model of Barndorff-Nielsen and Shephard. After a detailed theoretical study this model is estimated for some observed stock price series. As a further model with stochastic volatility multivariate continuous time GARCH (COGARCH) processes are introduced and their probabilistic and statistical properties are analysed.
Download or read book Multivariate Wishart Stochastic Volatility Models written by Bastian Gribisch and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Functionals of Multidimensional Diffusions with Applications to Finance written by Jan Baldeaux and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.
Download or read book Multivariate Stochastic Volatility with Co heteroscedasticity written by Joshua Chan and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multivariate Stochastic Volatility Models and Large Deviation Principles written by Archil Gulisashvili and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We establish a comprehensive sample path large deviation principle (LDP) for log-price processes associated with multivariate time-inhomogeneous stochastic volatility models. Examples of models for which the new LDP holds include Gaussian models, non-Gaussian fractional models, mixed models, models with reflection, and models in which the volatility process is a solution to a Volterra type stochastic integral equation. The sample path and small-noise LDPs for log-price processes are used to obtain large deviation style asymptotic formulas for the distribution function of the first exit time of a log-price process from an open set, multidimensional binary barrier options, call options, Asian options, and the implied volatility. Such formulas capture leading order asymptotics of the above-mentioned important quantities arising in the theory of stochastic volatility models. We also prove a sample path LDP for solutions to Volterra type stochastic integral equations with predictable coefficients depending on auxiliary stochastic processes.
Download or read book Multivariate Stochastic Volatility Models with Correlated Errors written by David X. Chan and published by . This book was released on 2008 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a Bayesian approach for parsimoniously estimating the correlation structure of the errors in a multivariate stochastic volatility model. Since the number of parameters in the joint correlation matrix of the return and volatility errors is potentially very large, we impose a prior that allows the off-diagonal elements of the inverse of the correlation matrix to be identically zero. The model is estimated using a Markov chain simulation method that samples from the posterior distribution of the volatilities and parameters. We illustrate the approach using both simulated and real examples. In the real examples, the method is applied to equities at three levels of aggregation: returns for firms within the same industry, returns for different industries and returns aggregated at the index level. We find pronounced correlation effects only at the highest level of aggregation.
Download or read book Stochastic Volatility written by Neil Shephard and published by OUP Oxford. This book was released on 2005-03-10 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This book brings together some of the main papers that have influenced the field of the econometrics of stochastic volatility, and shows that the development of this subject has been highly multidisciplinary, with results drawn from financial economics, probability theory, and econometrics, blending to produce methods and models that have aided our understanding of the realistic pricing of options, efficient asset allocation, and accurate risk assessment. A lengthy introduction by the editor connects the papers with the literature.
Download or read book Multivariate Stochastic Volatility Models written by Jun Yu and published by . This book was released on 2004 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shows that fully likelihood-based estimation and comparison of multivariate stochastic volatility (SV) models can be easily performed via a freely available Bayesian software called WinBUGS.
Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.
Download or read book Multivariate Stochastic Volatility written by Esfandiar Maasoumi and published by . This book was released on 2006 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essays on Multivariate Stochastic Volatility Models written by Sebastian Trojan and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first essay describes a very general stochastic volatility (SV) model specification with leverage, heavy tails, skew and switching regimes, using realized volatility (RV) as an auxiliary time series to improve inference on latent volatility. The information content of the range and of implied volatility using the VIX index is also analyzed. Database is the S & P 500 index. Asymmetry in the observation error is modeled by the generalized hyperbolic skew Student-t distribution, whose heavy and light tail enable substantial skewness. Resulting number of regimes and dynamics differ dependent on the auxiliary volatility proxy and are investigated in-sample for the financial crash period 2008/09 in more detail. An out-of-sample study comparing predictive ability of various model variants for a calm and a volatile period yields insights about the gains on forecasting performance from different volatility proxies. Results indicate that including RV or the VIX pays off mostly in more volatile market conditions, whereas in calmer environments SV specifications using no auxiliary series outperform. The range as volatility proxy provides a superior in-sample fit, but its predictive performance is found to be weak. The second essay presents a high frequency stochastic volatility model. Price duration and associated absolute price change in event time are modeled contemporaneously to fully capture volatility on the tick level, combining the SV and stochastic conditional duration (SCD) model. Estimation is with IBM stock intraday data 2001/10 (decimalization completed), taking a minimum midprice threshold of a half tick. Persistent information flow is extracted, featuring a positively correlated innovation term and negative cross effects in the AR(1) persistence matrix. Additionally, regime switching in both duration and absolute price change is introduced to increase nonlinear capabilities of the model. Thereby, a separate price jump.
Download or read book Multivariate Stochastic Volatility Models written by Jón Daníelsson and published by . This book was released on 1996 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Volatility Modeling and Analysis Via Coupled Wishart Process written by Zhong She and published by . This book was released on 2013 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
