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Author: Wolfgang Rinnergschwentner
Publisher:
ISBN:
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Languages : en
Pages : 36
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Author: Wolfgang Rinnergschwentner
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Author: Alexander Philipov
Publisher:
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Category :
Languages : en
Pages : 57
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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.
Author: Yu-Cheng Ku
Publisher:
ISBN:
Category :
Languages : en
Pages : 87
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Author: Roberto Casarin
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Languages : en
Pages : 0
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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.
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Languages : en
Pages :
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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.
Author: Bastian Gribisch
Publisher:
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Category :
Languages : en
Pages :
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Author: Jan Baldeaux
Publisher: Springer Science & Business Media
ISBN: 3319007475
Category : Mathematics
Languages : en
Pages : 432
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Book Description
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.
Author: Joshua Chan
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Category :
Languages : en
Pages :
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Author: Archil Gulisashvili
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Category :
Languages : en
Pages : 0
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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.
Author: David X. Chan
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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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.
