Time-change and Control of Stochastic Volatility
Author | : Adriana Ocejo Monge |
Publisher | : |
Total Pages | : |
Release | : 2014 |
Genre | : |
ISBN | : |
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Author | : Adriana Ocejo Monge |
Publisher | : |
Total Pages | : |
Release | : 2014 |
Genre | : |
ISBN | : |
Author | : Svetlana Borovkova |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : |
ISBN | : |
ABSTRACT. Using a powerful technique of stochastic time change, we introduce a new two factor commodity price model, where one of the fundamental factors is the activity rate of the stochastic clock. This factor implicitly introduces stochastic volatility into the model. The model is developed under both physical and risk neutral probability measures, which allows for a wide range of applications ranging from derivatives pricing to risk management.
Author | : John R. Birge |
Publisher | : Elsevier |
Total Pages | : 1026 |
Release | : 2007-11-16 |
Genre | : Business & Economics |
ISBN | : 9780080553252 |
The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.
Author | : Ole E Barndorff-nielsen |
Publisher | : World Scientific Publishing Company |
Total Pages | : 345 |
Release | : 2015-05-07 |
Genre | : Business & Economics |
ISBN | : 9814678600 |
Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance.In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.
Author | : Luc Bauwens |
Publisher | : John Wiley & Sons |
Total Pages | : 566 |
Release | : 2012-03-22 |
Genre | : Business & Economics |
ISBN | : 1118272056 |
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 | : Christian Kahl |
Publisher | : Universal-Publishers |
Total Pages | : 219 |
Release | : 2008 |
Genre | : Business & Economics |
ISBN | : 1581123833 |
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 | : Robert J. Elliot |
Publisher | : World Scientific |
Total Pages | : 605 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9814383309 |
This Festschrift is dedicated to Robert J Elliott on the occasion of his 70th birthday It brings together a collection of chapters by distinguished and eminent scholars in the fields of stochastic processes, filtering and control, as well as their applications to mathematical finance It presents cutting edge developments in these fields and is a valuable source of references for researchers, graduate students and market practitioners in mathematical finance and financial engineering Topics include the theory of stochastic processes, differential and stochastic games, mathematical finance, filtering and control.
Author | : Jesús Fernández-Villaverde |
Publisher | : |
Total Pages | : 72 |
Release | : 2010 |
Genre | : Business cycles |
ISBN | : |
This paper compares the role of stochastic volatility versus changes in monetary policy rules in accounting for the time-varying volatility of U.S. aggregate data. Of special interest to the authors is understanding the sources of the great moderation of business cycle fluctuations that the U.S. economy experienced between 1984 and 2007. To explore this issue, the authors build a medium-scale dynamic stochastic general equilibrium (DSGE) model with both stochastic volatility and parameter drifting in the Taylor rule and they estimate it non-linearly using U.S. data and Bayesian methods. Methodologically, the authors show how to confront such a rich model with the data by exploiting the structure of the high-order approximation to the decision rules that characterize the equilibrium of the economy. Their main empirical findings are: 1) even after controlling for stochastic volatility (and there is a fair amount of it), there is overwhelming evidence of changes in monetary policy during the analyzed period; 2) however, these changes in monetary policy mattered little for the great moderation; 3) most of the great performance of the U.S. economy during the 1990s was a result of good shocks; and 4) the response of monetary policy to inflation under Burns, Miller, and Greenspan was similar, while it was much higher under Volcker.
Author | : Andrey Sarychev |
Publisher | : Springer Science & Business Media |
Total Pages | : 418 |
Release | : 2009-03-31 |
Genre | : Mathematics |
ISBN | : 354069532X |
Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to ”real life” problems, as is the case in robotics, control of industrial processes or ?nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.
Author | : Jiuping Xu |
Publisher | : Springer |
Total Pages | : 837 |
Release | : 2019-06-19 |
Genre | : Technology & Engineering |
ISBN | : 3030212483 |
This book gathers the proceedings of the 13th International Conference on Management Science and Engineering Management (ICMSEM 2019), which was held at Brock University, Ontario, Canada on August 5–8, 2019. Exploring the latest ideas and pioneering research achievements in management science and engineering management, the respective contributions highlight both theoretical and practical studies on management science and computing methodologies, and present advanced management concepts and computing technologies for decision-making problems involving large, uncertain and unstructured data. Accordingly, the proceedings offer researchers and practitioners in related fields an essential update, as well as a source of new research directions.