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Mcmc Bayesian Estimation of a Skew-Ged Stochastic Volatility Model

Mcmc Bayesian Estimation of a Skew-Ged Stochastic Volatility Model
Author: Nunzio Cappuccio
Publisher:
Total Pages: 35
Release: 2003
Genre:
ISBN:

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In this paper we present a stochastic volatility model assuming that the return shock has a Skew-GED distribution. This allows a parsimonious yet flexible treatment of asymmetry and heavy tails in the conditional distribution of returns. The Skew-GED distribution nests both the GED, the Skew-normal and the normal densities as special cases so that specification tests are easily performed. Inference is conducted under a Bayesian framework using Markov Chain MonteCarlo methods for computing the posterior distributions of the parameters. More precisely, our Gibbs-MH updating scheme makes use of the Delayed Rejection Metropolis-Hastings methodology as proposed by Tierney and Mira (1999), and of Adaptive-Rejection Metropolis sampling. We apply this methodology to a data set of daily and weekly exchange rates. Our results suggest that daily returns are mostly symmetric with fat-tailed distributions while weekly returns exhibit both significant asymmetry and fat tails.


Stochastic Volatility and Realized Stochastic Volatility Models

Stochastic Volatility and Realized Stochastic Volatility Models
Author: Makoto Takahashi
Publisher: Springer Nature
Total Pages: 120
Release: 2023-04-18
Genre: Business & Economics
ISBN: 981990935X

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This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.


Bayesian Stochastic Volatility Models

Bayesian Stochastic Volatility Models
Author: Stefanos Giakoumatos
Publisher: LAP Lambert Academic Publishing
Total Pages: 240
Release: 2010-08
Genre:
ISBN: 9783838386331

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The phenomenon of changing variance and covariance is often encountered in financial time series. As a result, during the last years researchers focused on the time-varying volatility models. These models are able to describe the main characteristics of the financial data such as the volatility clustering. In addition, the development of the Markov Chain Monte Carlo Techniques (MCMC) provides a powerful tool for the estimation of the parameters of the time-varying volatility models, in the context of Bayesian analysis. In this thesis, we adopt the Bayesian inference and we propose easy-to-apply MCMC algorithms for a variety of time-varying volatility models. We use a recent development in the context of the MCMC techniques, the Auxiliary variable sampler. This technique enables us to construct MCMC algorithms, which only consist of Gibbs steps. We propose new MCMC algorithms for many univariate and multivariate models. Furthermore, we apply the proposed MCMC algorithms to real data and compare the above models based on their predictive distribution


The Skew-Normal and Related Families

The Skew-Normal and Related Families
Author: Adelchi Azzalini
Publisher: Cambridge University Press
Total Pages: 271
Release: 2013-12-19
Genre: Mathematics
ISBN: 1107729319

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Interest in the skew-normal and related families of distributions has grown enormously over recent years, as theory has advanced, challenges of data have grown, and computational tools have made substantial progress. This comprehensive treatment, blending theory and practice, will be the standard resource for statisticians and applied researchers. Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, the book is accessible to the wide range of researchers who use statistical modelling techniques. Guiding readers through the main concepts and results, it covers both the probability and the statistics sides of the subject, in the univariate and multivariate settings. The theoretical development is complemented by numerous illustrations and applications to a range of fields including quantitative finance, medical statistics, environmental risk studies, and industrial and business efficiency. The author's freely available R package sn, available from CRAN, equips readers to put the methods into action with their own data.


Modeling Stochastic Volatility with Application to Stock Returns

Modeling Stochastic Volatility with Application to Stock Returns
Author: Mr.Noureddine Krichene
Publisher: International Monetary Fund
Total Pages: 30
Release: 2003-06-01
Genre: Business & Economics
ISBN: 1451854846

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A stochastic volatility model where volatility was driven solely by a latent variable called news was estimated for three stock indices. A Markov chain Monte Carlo algorithm was used for estimating Bayesian parameters and filtering volatilities. Volatility persistence being close to one was consistent with both volatility clustering and mean reversion. Filtering showed highly volatile markets, reflecting frequent pertinent news. Diagnostics showed no model failure, although specification improvements were always possible. The model corroborated stylized findings in volatility modeling and has potential value for market participants in asset pricing and risk management, as well as for policymakers in the design of macroeconomic policies conducive to less volatile financial markets.


Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods

Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods
Author: Milan Fičura
Publisher:
Total Pages: 25
Release: 2015
Genre:
ISBN:

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We are comparing two approaches for stochastic volatility and jumps estimation in the EUR/USD time series - the non-parametric power-variation approach using high-frequency returns, and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We find that both of the methods do identify continuous stochastic volatility similarly, but they do not identify similarly the jump component. Firstly - the jumps estimated using the non-parametric high-frequency estimators are much more numerous than in the case of the Bayesian method using daily data. More importantly - we find that the probabilities of jump occurrences assigned to every day by both of the methods are virtually no rank-correlated (Spearman rank correlation is 0.0148) meaning that the two methods do not identify jumps at the same days. Actually the jump probabilities inferred using the non-parametric approach are not much correlated even with the daily realized variance and the daily squared returns, indicating that the discontinuous price changes (jumps) observed on high-frequencies may not be distinguishable (from the continuous volatility) on the daily frequency. As an additional result we find strong evidence for jump size dependence and jump clustering (based on the self-exciting Hawkes process) of the jumps identified using the non-parametric method (the shrinkage estimator).


Multivariate Stochastic Volatility Models

Multivariate Stochastic Volatility Models
Author: Jun Yu
Publisher:
Total Pages: 29
Release: 2004
Genre: Bayesian statistical decision theory
ISBN:

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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.


Bayesian Analysis of Moving Average Stochastic Volatility Models

Bayesian Analysis of Moving Average Stochastic Volatility Models
Author: Stefanos Dimitrakopoulos
Publisher:
Total Pages: 28
Release: 2017
Genre:
ISBN:

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We propose a moving average stochastic volatility in mean model and a moving average stochastic volatility model with leverage. For parameter estimation, we develop efficient Markov chain Monte Carlo algorithms and illustrate our methods, using simulated data and a real data set. We compare the proposed specifications against several competing stochastic volatility models, using marginal likelihoods and the observed-data Deviance information criterion. We find that the moving average stochastic volatility model with leverage has better fit to our daily return series than various standard benchmarks.