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Author: Anatoliy V. Swishchuk Publisher: ISBN: Category : Languages : en Pages : 76
Book Description
We consider multi-factor Levy models based on SDEs driven by alpha-stable Levy processes.Using change of time method for Levy-based stochastic integrals we show how to pricing many of financial and energy derivatives.
Author: Anatoliy V. Swishchuk Publisher: ISBN: Category : Languages : en Pages : 76
Book Description
We consider multi-factor Levy models based on SDEs driven by alpha-stable Levy processes.Using change of time method for Levy-based stochastic integrals we show how to pricing many of financial and energy derivatives.
Author: Anatoliy Swishchuk Publisher: World Scientific ISBN: 9814440140 Category : Business & Economics Languages : en Pages : 326
Book Description
Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Levy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S&P60 Canada Index, S&P500 Index and AECO Natural Gas Index.
Author: Alex Levin Publisher: ISBN: Category : Languages : en Pages : 31
Book Description
There is extensive empirical evidence that historical distributions of daily changes for stock prices, interest rates, foreign exchange rates, commodity prices and other underlyings have high peaks, heavy tails and non-zero skewness contrary to the normal distribution. These risk factors exhibit jumps, their volatility varies stochastically with clustering. Above distributional properties have significant impact on Risk Management, specifically on Value-at-Risk (VaR) calculations.This paper presents a class of multivariate models with the stochastic variance driven by Levy processes. The models with correlation structure in the stochastic variance allow for different shape and tail behavior of the marginal risk factor distributions, exact fit into the risk factor correlation structure, and proper non-linear scaling of VaR for different holding periods.In one-dimensional case, a pure jump Gamma process and other Levy processes for the stochastic variance are derived from the Maximum Entropy principle. Corresponding stochastic processes for the risk factors possess marginal distributions with wide range of heavy tails, from exponential to polynomial. Ornstein-Uhlenbeck type processes for the stochastic variance and corresponding term structure of the risk factor kurtosis and quantiles are investigated. In multi-dimensional case, the effective calibration and Monte Carlo simulation procedures are considered. Presented empirical evidence for different markets confirms a good agreement between the model and actual historical risk factor distributions.
Author: Frank J. Fabozzi Publisher: John Wiley & Sons ISBN: 0471445657 Category : Business & Economics Languages : en Pages : 914
Book Description
Expert advice that applies the theory and practice of investment management to today's financial environment The changing nature and rapid growth of the investment management industry, along with new theoretical developments in the field of finance, have led to a need for higher quality investment management practices and better qualified professionals. The Theory and Practice of Investment Management recognizes these needs and addresses them with sharp, innovative insights from some of the most respected experts in the field of investment management. The Theory and Practice of Investment Management discusses and describes the full scope of investment products and strategies available in today's market. Led by financial experts Frank Fabozzi and Harry Markowitz, the contributors to this book are active, successful practitioners with hands-on expertise. By combining real-world financial knowledge with investment management theory, this book provides a complete analysis of all pertinent investment products-including hedge funds and private equity-and explores a wide range of investment strategies. Tying together theoretical advances in investment management with actual applications, this book gives readers an opportunity to use proven investment management techniques to protect and grow a portfolio under many different circumstances.
Author: Joerg Kienitz Publisher: John Wiley & Sons ISBN: 0470744898 Category : Business & Economics Languages : en Pages : 736
Book Description
Financial modelling Theory, Implementation and Practice with MATLAB Source Jörg Kienitz and Daniel Wetterau Financial Modelling - Theory, Implementation and Practice with MATLAB Source is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk-neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes. Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk. The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor market model. Source code used for producing the results and analysing the models is provided on the author's dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981.
Author: Svetlozar T. Rachev Publisher: John Wiley & Sons ISBN: 0470937262 Category : Business & Economics Languages : en Pages : 316
Book Description
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: David R. Wood Publisher: Springer Nature ISBN: 3031474171 Category : Electronic books Languages : en Pages : 905
Book Description
MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-2 weeks in duration. This book is a scientific record of the 24 programs held at MATRIX in 2021-2022, including tandem workshops with Mathematisches Forschungsinstitut Oberwolfach (MFO), with Research Institute for Mathematical Sciences Kyoto University (RIMS), and with Sydney Mathematical Research Institute (SMRI).
Author: Damiano Brigo Publisher: Springer Science & Business Media ISBN: 354034604X Category : Mathematics Languages : en Pages : 1016
Book Description
The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.
Author: Malcolm Torry Publisher: Edward Elgar Publishing ISBN: 1803920963 Category : Political Science Languages : en Pages : 386
Book Description
Highlighting the diversity and complexity of the global Basic Income debate, Malcolm Torry assesses the history, current state, and future of research in this important field. Each chapter offers a concise history of a particular subfield of Basic Income research, describes the current state of research in that area, and makes proposals for the research required if the increasingly widespread global debate on Basic Income is to be constructive.
Author: Anatoliy V. Swishchuk
Author: Anatoliy V. Swishchuk
Author: Anatoliy Swishchuk
Author: Alex Levin
Author: Frank J. Fabozzi
Author: Joerg Kienitz
Author: Svetlozar T. Rachev
Author: Rainer Schwabe
Author: David R. Wood
Author: Damiano Brigo
Author: Malcolm Torry