A New Class Of Discrete Time Stochastic Volatility Model With Correlated Errors
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A New Class Of Discrete Time Stochastic Volatility Model With Correlated Errors
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Author : Sujay Mukhoti
language : en
Publisher:
Release Date : 2017
A New Class Of Discrete Time Stochastic Volatility Model With Correlated Errors written by Sujay Mukhoti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining features of the relationship between the return and its volatility. Among one of the earliest SVM, Taylor (1982) proposed a hierarchical model, where the current return is a function of the current latent volatility, which is further modeled as an auto-regressive process. In an attempt to make the SVMs more appropriate for complex realistic market behavior, a leverage parameter was introduced in the Taylor's SVM, which however led to the violation of the efficient market hypothesis (EMH, a necessary mean-zero condition for the return distribution that prevents arbitrage possibilities). Subsequently, a host of alternative SVMs had been developed and are currently in use. In this paper, we propose mean-corrections for several generalizations of Taylor's SVM that capture the complex market behavior as well as satisfy EMH. We also establish a few theoretical results to characterize the key desirable features of these models, and present comparison with other popular competitors. Furthermore, four real-life examples (Oil price, CITI bank stock price, Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the performance of this new class of SVMs.
Discrete Time Stochastic Volatility Model
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Author : Guojing Tang
language : en
Publisher:
Release Date : 2009
Discrete Time Stochastic Volatility Model written by Guojing Tang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
A Stochastic Volatility Model With Realized Measures For Option Pricing
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Author : Giacomo Bormetti
language : en
Publisher:
Release Date : 2019
A Stochastic Volatility Model With Realized Measures For Option Pricing written by Giacomo Bormetti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence - the crucial parameter in pricing Standard and Poor's 500 Index options.
Handbook Of Volatility Models And Their Applications
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Author : Luc Bauwens
language : en
Publisher: John Wiley & Sons
Release Date : 2012-04-17
Handbook Of Volatility Models And Their Applications written by Luc Bauwens and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-17 with Business & Economics categories.
A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.
Multivariate Stochastic Volatility Models With Correlated Errors
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Author : David X. Chan
language : en
Publisher:
Release Date : 2008
Multivariate Stochastic Volatility Models With Correlated Errors written by David X. Chan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
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.
Stochastic Volatility And Realized Stochastic Volatility Models
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Author : Makoto Takahashi
language : en
Publisher: Springer Nature
Release Date : 2023-04-18
Stochastic Volatility And Realized Stochastic Volatility Models written by Makoto Takahashi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-18 with Business & Economics categories.
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.
Modeling Stochastic Volatility With Application To Stock Returns
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Author : Mr.Noureddine Krichene
language : en
Publisher: International Monetary Fund
Release Date : 2003-06-01
Modeling Stochastic Volatility With Application To Stock Returns written by Mr.Noureddine Krichene and has been published by International Monetary Fund this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-01 with Business & Economics categories.
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.
Vix Computation Based On Affine Stochastic Volatility Models In Discrete Time
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Author : Asmerilda Hitaj
language : en
Publisher:
Release Date : 2015
Vix Computation Based On Affine Stochastic Volatility Models In Discrete Time written by Asmerilda Hitaj and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. We build this class of models in order to reach two desirable results. Firstly, we have a recursive procedure for the characteristic function of the log price at maturity that allows a semi-analytical formula for option prices as in Heston and Nandi (2000). Secondly, we try to reproduce some features of the VIX Index. We derive a simple formula for the VIX index and use it for option pricing purposes.
Non Stationary Stochastic Volatility Model For Dynamic Feedback And Skewness
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Author : Sujay Mukhoti
language : en
Publisher:
Release Date : 2015
Non Stationary Stochastic Volatility Model For Dynamic Feedback And Skewness written by Sujay Mukhoti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
In this paper I present a new single factor stochastic volatility model for asset return observed in discrete time and its latent volatility. This model unifies the feedback effect and return skewness using a common factor for return and its volatility. Further, it generalizes the existing stochastic volatility framework with constant feedback to one with time varying feedback and as a consequence time varying skewness follows. However, presence of dynamic feedback effect violates the weak-stationarity assumption usually considered for the latent volatility process. The concept of bounded stationarity has been proposed in this paper to address the issue of non-stationarity. A characterization of the error distributions for returns and volatility is provided on the basis of existence of conditional moments. Finally, an application of the model has been explained using S&P100 daily returns under the assumption of Normal error and half Normal common factor distribution.
Discrete Time Stochastic Volatility Models And Mcmc Based Statistical Inference
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Author : Nikolaus Hautsch
language : en
Publisher:
Release Date : 2008
Discrete Time Stochastic Volatility Models And Mcmc Based Statistical Inference written by Nikolaus Hautsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.