Parameter Estimation In Stochastic Volatility Models

Author : Jaya P. N. Bishwal
Publisher : Springer Nature
Page : 634 pages
File Size : 55,6 Mb
Release : 2022-08-06
Category : Mathematics
ISBN : 9783031038617

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Parameter Estimation in Stochastic Volatility Models by Jaya P. N. Bishwal Pdf

This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Author : Ibukun O.O. Amusan
Publisher : Unknown
Page : 0 pages
File Size : 40,5 Mb
Release : 2013
Category : Electronic
ISBN : OCLC:1404790668

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Parameter estimation for a stochastic volatility model with coupled additive and multiplicative noise by Ibukun O.O. Amusan Pdf

Author : Makoto Takahashi,Yasuhiro Omori,Toshiaki Watanabe
Publisher : Springer Nature
Page : 120 pages
File Size : 53,9 Mb
Release : 2023-04-18
Category : Business & Economics
ISBN : 9789819909353

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Stochastic Volatility and Realized Stochastic Volatility Models by Makoto Takahashi,Yasuhiro Omori,Toshiaki Watanabe Pdf

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.

Author : Yacine Aït-Sahalia,Robert Kimmel
Publisher : Unknown
Page : 42 pages
File Size : 55,9 Mb
Release : 2004
Category : Options (Finance)
ISBN : OCLC:249834367

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Maximum Likelihood Estimation of Stochastic Volatility Models by Yacine Aït-Sahalia,Robert Kimmel Pdf

We develop and implement a new method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by the implied volatility of a short dated at-the-money option. We find that the approximation results in a negligible loss of accuracy. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine model of Heston (1993) and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.

Author : Sassan Alizadeh,Michael W. Brandt,Francis X. Diebold
Publisher : Unknown
Page : 82 pages
File Size : 42,5 Mb
Release : 2001
Category : Economics
ISBN : PSU:000044882532

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High- and Low-frequency Exchange Rate Volatility Dynamics by Sassan Alizadeh,Michael W. Brandt,Francis X. Diebold Pdf

We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that the range is not only a highly efficient volatility proxy, but also that it is approximately Gaussian and robust to microstructure noise. The good properties of the range imply that range-based Gaussian quasi-maximum likelihood estimation produces simple and highly efficient estimates of stochastic volatility models and extractions of latent volatility series. We use our method to examine the dynamics of daily exchange rate volatility and discover that traditional one-factor models are inadequate for describing simultaneously the high- and low-frequency dynamics of volatility. Instead, the evidence points strongly toward two-factor models with one highly persistent factor and one quickly mean-reverting factor.

Author : Mr.Noureddine Krichene
Publisher : International Monetary Fund
Page : 30 pages
File Size : 47,7 Mb
Release : 2003-06-01
Category : Business & Economics
ISBN : 9781451854848

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Modeling Stochastic Volatility with Application to Stock Returns by Mr.Noureddine Krichene Pdf

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.

Author : Steven Cannon Hogan
Publisher : Unknown
Page : 246 pages
File Size : 45,5 Mb
Release : 2000
Category : Electronic
ISBN : CORNELL:31924087289918

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Nonparametric Estimation of Stochastic Volatility Models by Steven Cannon Hogan Pdf

Author : Jaya P. N. Bishwal
Publisher : Springer
Page : 268 pages
File Size : 54,8 Mb
Release : 2007-09-26
Category : Mathematics
ISBN : 9783540744481

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Parameter Estimation in Stochastic Differential Equations by Jaya P. N. Bishwal Pdf

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Author : Luc Bauwens,Christian M. Hafner,Sebastien Laurent
Publisher : John Wiley & Sons
Page : 566 pages
File Size : 49,9 Mb
Release : 2012-03-22
Category : Business & Economics
ISBN : 9781118272053

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Handbook of Volatility Models and Their Applications by Luc Bauwens,Christian M. Hafner,Sebastien Laurent Pdf

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.

Author : Jon Danielsson
Publisher : Unknown
Page : 254 pages
File Size : 44,8 Mb
Release : 1991
Category : Pricing
ISBN : OCLC:24332896

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Estimation of the Dynamic Stochastic Volatility Model for Asset Price Determination by Simulated Maximum Likelihood by Jon Danielsson Pdf

Author : Fabrice D. Rouah,Gregory Vainberg
Publisher : John Wiley & Sons
Page : 456 pages
File Size : 46,6 Mb
Release : 2012-06-15
Category : Business & Economics
ISBN : 9781118429204

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Option Pricing Models and Volatility Using Excel-VBA by Fabrice D. Rouah,Gregory Vainberg Pdf

This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book. Praise for Option Pricing Models & Volatility Using Excel-VBA "Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers." —Peter Christoffersen, Associate Professor of Finance, Desautels Faculty of Management, McGill University "This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library." —Espen Gaarder Haug, option trader, philosopher, and author of Derivatives Models on Models "I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH." —Steven L. Heston, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland

Author : Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko
Publisher : Springer
Page : 390 pages
File Size : 45,8 Mb
Release : 2018-01-04
Category : Mathematics
ISBN : 9783319710303

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Parameter Estimation in Fractional Diffusion Models by Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko Pdf

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

Author : Jude Hemanth,Tuncay Yigit,Bogdan Patrut,Anastassia Angelopoulou
Publisher : Springer Nature
Page : 797 pages
File Size : 45,8 Mb
Release : 2021-07-05
Category : Computers
ISBN : 9783030793579

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Trends in Data Engineering Methods for Intelligent Systems by Jude Hemanth,Tuncay Yigit,Bogdan Patrut,Anastassia Angelopoulou Pdf

This book briefly covers internationally contributed chapters with artificial intelligence and applied mathematics-oriented background-details. Nowadays, the world is under attack of intelligent systems covering all fields to make them practical and meaningful for humans. In this sense, this edited book provides the most recent research on use of engineering capabilities for developing intelligent systems. The chapters are a collection from the works presented at the 2nd International Conference on Artificial Intelligence and Applied Mathematics in Engineering held within 09-10-11 October 2020 at the Antalya, Manavgat (Turkey). The target audience of the book covers scientists, experts, M.Sc. and Ph.D. students, post-docs, and anyone interested in intelligent systems and their usage in different problem domains. The book is suitable to be used as a reference work in the courses associated with artificial intelligence and applied mathematics.

Author : Neil Shephard
Publisher : Oxford University Press on Demand
Page : 534 pages
File Size : 49,9 Mb
Release : 2005
Category : Business & Economics
ISBN : 9780199257201

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Stochastic Volatility by Neil Shephard Pdf

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 work brings together some of the main papers that have influenced this field, andshows that the development of this subject has been highly multidisciplinary.

Author : Yong Zeng,Shu Wu
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 44,7 Mb
Release : 2013-08-15
Category : Business & Economics
ISBN : 9781461477891

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State-Space Models by Yong Zeng,Shu Wu Pdf

State-space models as an important mathematical tool has been widely used in many different fields. This edited collection explores recent theoretical developments of the models and their applications in economics and finance. The book includes nonlinear and non-Gaussian time series models, regime-switching and hidden Markov models, continuous- or discrete-time state processes, and models of equally-spaced or irregularly-spaced (discrete or continuous) observations. The contributed chapters are divided into four parts. The first part is on Particle Filtering and Parameter Learning in Nonlinear State-Space Models. The second part focuses on the application of Linear State-Space Models in Macroeconomics and Finance. The third part deals with Hidden Markov Models, Regime Switching and Mathematical Finance and the fourth part is on Nonlinear State-Space Models for High Frequency Financial Data. The book will appeal to graduate students and researchers studying state-space modeling in economics, statistics, and mathematics, as well as to finance professionals.