Financial Models With Levy Processes And Volatility Clustering
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| Author | : Svetlozar T. Rachev |
| Publisher | : John Wiley & Sons |
| Total Pages | : 316 |
| Release | : 2011-02-08 |
| Genre | : Business & Economics |
| ISBN | : 0470937262 |
An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential Lévy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.
| Author | : Donatien Hainaut |
| Publisher | : |
| Total Pages | : 34 |
| Release | : 2016 |
| Genre | : |
| ISBN | : |
This work contributes to the literature over time-changed processes in two directions. Firstly, this is the first thorough study of theoretical properties of Lévy processes, subordinated by a self-excited random clock. The process observed on this new time scale, called clustered Lévy process, presents interesting features for financial modeling like stochastic volatility and grouped jumps. In this framework, we infer analytical expressions for the mean, variance, and a new parametric form of the moment generating function. A bivariate extension is also considered. Furthermore, this article introduces a class of exponential affine changes of measure and the necessary conditions to preserve the dynamics of clustered Lévy processes under an equivalent measure. The second major contribution is empirical. A new particle filter is proposed so as to recover the market time scale from a time series. And a method based on the numerical inversion of the moment generating function is used to estimate parameters. Finally, a numerical analysis reveals that random clocks driving the S&P 500 and Eurostoxx 50 indices are highly correlated to trading volumes.
| Author | : Constantin Zopounidis |
| Publisher | : John Wiley & Sons |
| Total Pages | : 451 |
| Release | : 2015-05-06 |
| Genre | : Business & Economics |
| ISBN | : 1118738403 |
A Comprehensive Guide to Quantitative Financial Risk Management Written by an international team of experts in the field, Quantitative Financial Risk Management: Theory and Practice provides an invaluable guide to the most recent and innovative research on the topics of financial risk management, portfolio management, credit risk modeling, and worldwide financial markets. This comprehensive text reviews the tools and concepts of financial management that draw on the practices of economics, accounting, statistics, econometrics, mathematics, stochastic processes, and computer science and technology. Using the information found in Quantitative Financial Risk Management can help professionals to better manage, monitor, and measure risk, especially in today's uncertain world of globalization, market volatility, and geo-political crisis. Quantitative Financial Risk Management delivers the information, tools, techniques, and most current research in the critical field of risk management. This text offers an essential guide for quantitative analysts, financial professionals, and academic scholars.
| Author | : Stefano M. Iacus |
| Publisher | : John Wiley & Sons |
| Total Pages | : 402 |
| Release | : 2011-02-23 |
| Genre | : Business & Economics |
| ISBN | : 1119990203 |
Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
| Author | : J.E. Trinidad-Segovia |
| Publisher | : MDPI |
| Total Pages | : 418 |
| Release | : 2021-02-12 |
| Genre | : Business & Economics |
| ISBN | : 3036501967 |
This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice.
| Author | : William Johnson |
| Publisher | : HiTeX Press |
| Total Pages | : 450 |
| Release | : 2024-10-17 |
| Genre | : Business & Economics |
| ISBN | : |
"Stochastic Calculus for Finance: A Practical Guide" offers an insightful exploration into the mathematical intricacies underpinning modern financial markets. Designed to demystify complex concepts, this comprehensive text bridges rigorous theory with application, crafting a resource that is as invaluable to students embarking on a financial career as it is to seasoned professionals seeking to enrich their analytical toolkit. Through an elegant synthesis of probability theory, stochastic processes, and advanced calculus, readers are introduced to the foundational frameworks that drive market analysis, derivative pricing, and portfolio optimization. This guide stands out by making sophisticated mathematical models accessible, without sacrificing depth or precision. By delving into topics such as Brownian motion, stochastic differential equations, and applications of machine learning, the book equips readers with the tools needed to navigate and innovate in the financial landscape. It elucidates the power of stochastic calculus in shaping strategies and solutions to real-world financial challenges, fostering a nuanced understanding of risk management and asset allocation. With its blend of theoretical insight and practical application, this book promises to be an essential companion for those dedicated to mastering the art and science of finance.
| Author | : Yuri Kabanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 553 |
| Release | : 2013-10-23 |
| Genre | : Mathematics |
| ISBN | : 3319020692 |
The present volume is dedicated to Marek Musiela, an eminent scholar and practitioner who is perhaps best-known for his important contributions to problems of derivative pricing, theory of term structure of interest rates, theory of defaultable securities and other topics in modern mathematical finance. It includes 25 research papers by 47 authors, established experts and newcomers alike, that cover the whole range of the "hot" topics in the discipline. The contributed articles not only give a clear picture about what is going on in this rapidly developing field of knowledge but provide methods ready for practical implementation. They also open new prospects for further studies in risk management, portfolio optimization and financial engineering.
| Author | : Cira Perna |
| Publisher | : Springer |
| Total Pages | : 190 |
| Release | : 2014-07-08 |
| Genre | : Business & Economics |
| ISBN | : 3319050141 |
This volume aims to collect new ideas presented in the form of 4 page papers dedicated to mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field and provides interesting scientific products in theoretical models and practical applications, as well as in scientific discussion of problems of national and international interest. This work reflects the results discussed at the biennial conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF), born at the University of Salerno in 2004.
| Author | : Michele Leonardo Bianchi |
| Publisher | : World Scientific |
| Total Pages | : 598 |
| Release | : 2019-03-08 |
| Genre | : Business & Economics |
| ISBN | : 9813276215 |
The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.
| 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.
