Simulation Methods for Levy-Driven Carma Stochastic Volatility Models PDF Download
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Author: George Tauchen
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
We develop simulation schemes for the new classes of non-Gaussian pure jump Levy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Levy process, which then makes series approximation methods directly applicable. These methods entail simulation of the Levy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function nor specification of a copula function. We also present a new, and apparently quite flexible, bivariate mixture of gammas model for the driving Levy process. Within this setup, it is quite straightforward to generate simulations from a Levy-driven CARMA stochastic volatility model augmented by a pure-jump price component. Simulations reveal the wide range of different types of financial price processes that can be generated in this manner, including processes with persistent stochastic volatility, dynamic leverage, and jumps.
Author: George Tauchen
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
We develop simulation schemes for the new classes of non-Gaussian pure jump Levy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Levy process, which then makes series approximation methods directly applicable. These methods entail simulation of the Levy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function nor specification of a copula function. We also present a new, and apparently quite flexible, bivariate mixture of gammas model for the driving Levy process. Within this setup, it is quite straightforward to generate simulations from a Levy-driven CARMA stochastic volatility model augmented by a pure-jump price component. Simulations reveal the wide range of different types of financial price processes that can be generated in this manner, including processes with persistent stochastic volatility, dynamic leverage, and jumps.
Author: Jaya P. N. Bishwal
Publisher: Springer Nature
ISBN: 3031038614
Category : Mathematics
Languages : en
Pages : 634
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Book Description
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:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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: Stefano M. Iacus
Publisher: Springer
ISBN: 3319555693
Category : Computers
Languages : en
Pages : 277
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Book Description
The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA, COGARCH, and Point processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these processes have been originally proposed in physics and more recently in finance, they are becoming popular also in biology due to the fact the time course experimental data are now available. The YUIMA package, available on CRAN, can be freely downloaded and this companion book will make the user able to start his or her analysis from the first page.
Author: Christian Kahl
Publisher: Universal-Publishers
ISBN: 1581123833
Category : Business & Economics
Languages : en
Pages : 219
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Book Description
The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.
Author: Luc Bauwens
Publisher: John Wiley & Sons
ISBN: 0470872519
Category : Business & Economics
Languages : en
Pages : 566
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Book Description
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: Ole E. Barndorff-Nielsen
Publisher: Springer
ISBN: 3319941291
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Drawing on advanced probability theory, Ambit Stochastics is used to model stochastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for this burgeoning field, complete with the applications that have driven its development. Unique to Ambit Stochastics are ambit sets, which allow the delimitation of space-time to a zone of interest, and ambit fields, which are particularly well-adapted to modelling stochastic volatility or intermittency. These attributes lend themselves notably to applications in the statistical theory of turbulence and financial econometrics. In addition to the theory and applications of Ambit Stochastics, the book also contains new theory on the simulation of ambit fields and a comprehensive stochastic integration theory for Volterra processes in a non-semimartingale context. Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical stochastic modelling.
Author: Samanta, Debabrata
Publisher: IGI Global
ISBN: 1799877035
Category : Computers
Languages : en
Pages : 277
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Book Description
With the field of computational statistics growing rapidly, there is a need for capturing the advances and assessing their impact. Advances in simulation and graphical analysis also add to the pace of the statistical analytics field. Computational statistics play a key role in financial applications, particularly risk management and derivative pricing, biological applications including bioinformatics and computational biology, and computer network security applications that touch the lives of people. With high impacting areas such as these, it becomes important to dig deeper into the subject and explore the key areas and their progress in the recent past. Methodologies and Applications of Computational Statistics for Machine Intelligence serves as a guide to the applications of new advances in computational statistics. This text holds an accumulation of the thoughts of multiple experts together, keeping the focus on core computational statistics that apply to all domains. Covering topics including artificial intelligence, deep learning, and trend analysis, this book is an ideal resource for statisticians, computer scientists, mathematicians, lecturers, tutors, researchers, academic and corporate libraries, practitioners, professionals, students, and academicians.
Author: Tata Subba Rao
Publisher: Elsevier
ISBN: 0444538585
Category : Mathematics
Languages : en
Pages : 778
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Book Description
'Handbook of Statistics' is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with volume 30 dealing with time series.
Author:
Publisher: Elsevier
ISBN: 0444538631
Category : Mathematics
Languages : en
Pages : 777
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Book Description
The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments.The Handbook of Statistics is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience. Comprehensively presents the various aspects of statistical methodology Discusses a wide variety of diverse applications and recent developments Contributors are internationally renowened experts in their respective areas
