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Author: Michail Korniotis Publisher: ISBN: 9781109509427 Category : Languages : en Pages : 179
Book Description
We propose a multi-factor stochastic model that can be used as a modeling tool in several areas of applied mathematics. Our modeling efforts are focused on addressing the basic characteristics of quantities that represent random rate of change. These characteristics include properties of their evolution pattern, cross-factor correlation, and the stochastic nature of their diffusion parameter. At the same time, we address the question of solutions implied by the model, as well as the model's tractability. The model is introduced in a general mathematical context, prior to any specific problem consideration. We choose this approach to stress the model's functional independence of any particular application. Within this framework, we are able to represent the evolution of quantities sensitive to random rates of change, as solutions of partial differential equations. We obtain solutions of the resulting partial differential equations by adopting a two-step solution method. The first step approximates the solution using perturbation methods. This procedure specifies the two leading terms as solutions of simpler differential problems. The second step allows us to derive explicit solutions for the terms using the eigenfunction expansion method. A computer algorithm for the solution was also built. This allowed the calibration of the model parameters and a comparison of fitness with existing models. The usefulness and flexibility of the model is demonstrated by considering applications in three areas of applied mathematics: Interest rate, credit risk, and mortality modeling. We comment on how our model generalizes existing models in these areas and its advantages over previously proposed models.
Author: Michail Korniotis Publisher: ISBN: 9781109509427 Category : Languages : en Pages : 179
Book Description
We propose a multi-factor stochastic model that can be used as a modeling tool in several areas of applied mathematics. Our modeling efforts are focused on addressing the basic characteristics of quantities that represent random rate of change. These characteristics include properties of their evolution pattern, cross-factor correlation, and the stochastic nature of their diffusion parameter. At the same time, we address the question of solutions implied by the model, as well as the model's tractability. The model is introduced in a general mathematical context, prior to any specific problem consideration. We choose this approach to stress the model's functional independence of any particular application. Within this framework, we are able to represent the evolution of quantities sensitive to random rates of change, as solutions of partial differential equations. We obtain solutions of the resulting partial differential equations by adopting a two-step solution method. The first step approximates the solution using perturbation methods. This procedure specifies the two leading terms as solutions of simpler differential problems. The second step allows us to derive explicit solutions for the terms using the eigenfunction expansion method. A computer algorithm for the solution was also built. This allowed the calibration of the model parameters and a comparison of fitness with existing models. The usefulness and flexibility of the model is demonstrated by considering applications in three areas of applied mathematics: Interest rate, credit risk, and mortality modeling. We comment on how our model generalizes existing models in these areas and its advantages over previously proposed models.
Author: Neil Shephard Publisher: Oxford University Press, USA ISBN: 0199257205 Category : Business & Economics Languages : en Pages : 534
Book Description
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: Robert Buff Publisher: Springer Science & Business Media ISBN: 3642563236 Category : Mathematics Languages : en Pages : 246
Book Description
This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.
Author: Luc Bauwens Publisher: John Wiley & Sons ISBN: 1118272056 Category : Business & Economics Languages : en Pages : 566
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: Lorenzo Bergomi Publisher: CRC Press ISBN: 1482244071 Category : Business & Economics Languages : en Pages : 520
Book Description
Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Author: Christian Bayer Publisher: SIAM ISBN: 1611977789 Category : Mathematics Languages : en Pages : 292
Book Description
Volatility underpins financial markets by encapsulating uncertainty about prices, individual behaviors, and decisions and has traditionally been modeled as a semimartingale, with consequent scaling properties. The mathematical description of the volatility process has been an active topic of research for decades; however, driven by empirical estimates of the scaling behavior of volatility, a new paradigm has emerged, whereby paths of volatility are rougher than those of semimartingales. According to this perspective, volatility behaves essentially as a fractional Brownian motion with a small Hurst parameter. The first book to offer a comprehensive exploration of the subject, Rough Volatility contributes to the understanding and application of rough volatility models by equipping readers with the tools and insights needed to delve into the topic, exploring the motivation for rough volatility modeling, providing a toolbox for computation and practical implementation, and organizing the material to reflect the subject’s development and progression. This book is designed for researchers and graduate students in quantitative finance as well as quantitative analysts and finance professionals.
Author: Jim Gatheral Publisher: John Wiley & Sons ISBN: 1118046455 Category : Business & Economics Languages : en Pages : 204
Book Description
Praise for The Volatility Surface "I'm thrilled by the appearance of Jim Gatheral's new book The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models--achieving remarkable clarity without giving up sophistication, depth, or breadth." --Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University "Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it." --Emanuel Derman, author of My Life as a Quant "Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form." --Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University "Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In The Volatility Surface he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility." --Paul Wilmott, author and mathematician "As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, The Volatility Surface gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it." --Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University "Jim Gatheral could not have written a better book." --Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP
Author: Mr.Noureddine Krichene Publisher: 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.
Author: Michail Korniotis
Author: Michail Korniotis
Author: Neil Shephard
Author: Robert Buff
Author: Luc Bauwens
Author: Lorenzo Bergomi
Author: Christian Bayer
Author: Susanna Wing Yan Kwok
Author: Jim Gatheral
Author: Damir Filipovic
Author: Mr.Noureddine Krichene