Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 43
Book Description
Calibration of Stochastic Volatility Models Using Particle Markov Chain Monte Carlo Methods
Author: Particle Markov Chain Monte Carlo for Stochastic Volatility Models
Author: Simon BodilsenMarkov Chain Monte Carlo Methods for Generalized Stochastic Volatility Models
Author: Siddhartha ChibPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
This paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy-tailed student-t distributions (with unknown degrees of freedom) and covariate effects in the observation and volatility equations and a jump component in the observation equation. By building on the work of Kim, Shephard and Chib (1998), we develop efficient Markov chain Monte Carlo algorithms for estimating these models. The paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods. Computation of the marginal likelihood by the method of Chib (1995) is also considered. The methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the S&P 500 index where several stochastic volatility models are formally compared under various priors on the parameters.
Estimation of Stochastic Volatility Models with Markov Chain Monte Carlo Methods
Author: Maximilian RichterPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Markov Chain Monte Carlo (MCMC) methods are a Bayesian approach to tackle one of the main obstacles encountered in the estimation of modern-day stochastic volatility models: the curse of dimensionality induced by the increasing number of latent variables. This thesis strives to study the performance of affine jump-diffusion models in comparison to state-of-the-art Lévy-based return dynamics. Thus MCMC methods are applied to a novel dataset of S & P500 returns that comprises different periods of economic turmoil, such as the subprime crisis. The subordinate research goal is to address difficulties in the implementation of the MCMC methodology. In line with previous studies, the results indicate that jump components are indeed crucial for capturing complex patterns like skewness and excess kurtosis of the return distributions. Moreover, infinite-activity Lévy jumps prove to be superior to discrete compound Poisson jumps.
Modeling Stochastic Volatility with Application to Stock Returns
Author: Mr.Noureddine KrichenePublisher: International Monetary Fund
ISBN: 1451854846
Category : Business & Economics
Languages : en
Pages : 30
Book Description
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.
Markov Chain Monte Carlo
Author: Dani GamermanPublisher: CRC Press
ISBN: 9781584885870
Category : Mathematics
Languages : en
Pages : 352
Book Description
While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration. Major changes from the previous edition: · More examples with discussion of computational details in chapters on Gibbs sampling and Metropolis-Hastings algorithms · Recent developments in MCMC, including reversible jump, slice sampling, bridge sampling, path sampling, multiple-try, and delayed rejection · Discussion of computation using both R and WinBUGS · Additional exercises and selected solutions within the text, with all data sets and software available for download from the Web · Sections on spatial models and model adequacy The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. The book will appeal to everyone working with MCMC techniques, especially research and graduate statisticians and biostatisticians, and scientists handling data and formulating models. The book has been substantially reinforced as a first reading of material on MCMC and, consequently, as a textbook for modern Bayesian computation and Bayesian inference courses.
The Efficient Markov Chain Monte Carlo Estimation of the Stochastic Volatility Model with Changing Regimes
Author: An An ChenPublisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 108
Book Description
Analysis of the Bitcoin Exchange Using Particle MCMC Methods
Author: Michael JohnsonPublisher:
ISBN:
Category :
Languages : en
Pages : 59
Book Description
Stochastic volatility models (SVM) are commonly used to model time series data. They have many applications in finance and are useful tools to describe the evolution of asset returns. The motivation for this project is to determine if stochastic volatility models can be used to model Bitcoin exchange rates in a way that can contribute to an effective trading strategy. We consider a basic SVM and several extensions that include fat tails, leverage, and covariate effects. The Bayesian approach with the particle Markov chain Monte Carlo (PMCMC) method is employed to estimate the model parameters. We assess the goodness of the estimated model using the deviance information criterion (DIC). Simulation studies are conducted to assess the performance of particle MCMC and to compare with the traditional MCMC approach. We then apply the proposed method to the Bitcoin exchange rate data and compare the effectiveness of each type of SVM.
Stochastic Volatility and Realized Stochastic Volatility Models
Author: Makoto TakahashiPublisher: Springer Nature
ISBN: 981990935X
Category : Business & Economics
Languages : en
Pages : 120
Book Description
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.
Advanced Markov Chain Monte Carlo Methods
Author: Faming LiangPublisher: John Wiley & Sons
ISBN: 1119956803
Category : Mathematics
Languages : en
Pages : 308
Book Description
Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial optimization, and computational physics. Key Features: Expanded coverage of the stochastic approximation Monte Carlo and dynamic weighting algorithms that are essentially immune to local trap problems. A detailed discussion of the Monte Carlo Metropolis-Hastings algorithm that can be used for sampling from distributions with intractable normalizing constants. Up-to-date accounts of recent developments of the Gibbs sampler. Comprehensive overviews of the population-based MCMC algorithms and the MCMC algorithms with adaptive proposals. This book can be used as a textbook or a reference book for a one-semester graduate course in statistics, computational biology, engineering, and computer sciences. Applied or theoretical researchers will also find this book beneficial.