Modelling And Simulation Of Stochastic Volatility In Finance
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Modelling And Simulation Of Stochastic Volatility In Finance
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Author : Christian Kahl
language : en
Publisher: Universal-Publishers
Release Date : 2008
Modelling And Simulation Of Stochastic Volatility In Finance written by Christian Kahl and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Business & Economics categories.
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.
Monte Carlo Methods In Finance
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Author : Peter Jäckel
language : de
Publisher: John Wiley & Sons
Release Date : 2002-04-03
Monte Carlo Methods In Finance written by Peter Jäckel and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-03 with Business & Economics categories.
Dieses Buch ist ein handlicher und praktischer Leitfaden zur Monte Carlo Simulation (MCS). Er gibt eine Einführung in Standardmethoden und fortgeschrittene Verfahren, um die zunehmende Komplexität derivativer Portfolios besser zu erfassen. Das hier behandelte Spektrum von MCS-Anwendungen reicht von der Preisbestimmung komplexerer Derivate, z.B. von amerikanischen und asiatischen Optionen, bis hin zur Messung des Value at Risk und zur Modellierung komplexer Marktdynamik. Anhand einer Vielzahl praktischer Beispiele wird erläutert, wie man Monte Carlo Methoden einsetzt. Dabei gehen die Autoren zunächst auf die Grundlagen und danach auf fortgeschrittene Techniken ein. Darüber hinaus geben sie nützliche Tipps und Hinweise für das Entwickeln und Arbeiten mit MCS-Methoden. Die Autoren sind Experten auf dem Gebiet der Monte Carlo Simulation und verfügen über langjährige Erfahrung im Umgang mit MCS-Methoden. Die Begleit-CD enthält Excel Muster Spreadsheets sowie VBA und C++ Code Snippets, die der Leser installieren und so mit den im Buch beschriebenen Beispiele frei experimentieren kann. "Monte Carlo Methods in Finance" - ein unverzichtbares Nachschlagewerk für quantitative Analysten, die bei der Bewertung von Optionspreisen und Riskmanagement auf Modelle zurückgreifen müssen.
Stochastic Simulation And Applications In Finance With Matlab Programs
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Author : Huu Tue Huynh
language : en
Publisher: John Wiley & Sons
Release Date : 2008-12-22
Stochastic Simulation And Applications In Finance With Matlab Programs written by Huu Tue Huynh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-22 with Business & Economics categories.
Stochastic Simulation and Applications in Finance with MATLAB Programs explains the fundamentals of Monte Carlo simulation techniques, their use in the numerical resolution of stochastic differential equations and their current applications in finance. Building on an integrated approach, it provides a pedagogical treatment of the need-to-know materials in risk management and financial engineering. The book takes readers through the basic concepts, covering the most recent research and problems in the area, including: the quadratic re-sampling technique, the Least Squared Method, the dynamic programming and Stratified State Aggregation technique to price American options, the extreme value simulation technique to price exotic options and the retrieval of volatility method to estimate Greeks. The authors also present modern term structure of interest rate models and pricing swaptions with the BGM market model, and give a full explanation of corporate securities valuation and credit risk based on the structural approach of Merton. Case studies on financial guarantees illustrate how to implement the simulation techniques in pricing and hedging. NOTE TO READER: The CD has been converted to URL. Go to the following website www.wiley.com/go/huyhnstochastic which provides MATLAB programs for the practical examples and case studies, which will give the reader confidence in using and adapting specific ways to solve problems involving stochastic processes in finance.
Derivatives In Financial Markets With Stochastic Volatility
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Author : Jean-Pierre Fouque
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-03
Derivatives In Financial Markets With Stochastic Volatility written by Jean-Pierre Fouque and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-03 with Business & Economics categories.
This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.
Statistical Tools For Finance And Insurance
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Author : Pavel Čižek
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Statistical Tools For Finance And Insurance written by Pavel Čižek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Business & Economics categories.
Statistical Tools in Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field, this book offers a unique combination of topics from which every market analyst and risk manager will benefit. Covering topics such as heavy tailed distributions, implied trinomial trees, support vector machines, valuation of mortgage-backed securities, pricing of CAT bonds, simulation of risk processes and ruin probability approximation, the book does not only offer practitioners insight into new methods for their applications, but it also gives theoreticians insight into the applicability of the stochastic technology. Additionally, the book provides the tools, instruments and (online) algorithms for recent techniques in quantitative finance and modern treatments in insurance calculations. Written in an accessible and engaging style, this self-instructional book makes a good use of extensive examples and full explanations. Thenbsp;design of the text links theory and computational tools in an innovative way. All Quantlets for the calculation of examples given in the text are supported by the academic edition of XploRe and may be executed via XploRe Quantlet Server (XQS). The downloadable electronic edition of the book enables one to run, modify, and enhance all Quantlets on the spot.
The Heston Model And Its Extensions In Vba
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Author : Fabrice D. Rouah
language : en
Publisher: John Wiley & Sons
Release Date : 2015-03-24
The Heston Model And Its Extensions In Vba written by Fabrice D. Rouah and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Business & Economics categories.
Practical options pricing for better-informed investment decisions. The Heston Model and Its Extensions in VBA is the definitive guide to options pricing using two of the derivatives industry's most powerful modeling tools—the Heston model, and VBA. Light on theory, this extremely useful reference focuses on implementation, and can help investors more efficiently—and accurately—exploit market information to better inform investment decisions. Coverage includes a description of the Heston model, with specific emphasis on equity options pricing and variance modeling, The book focuses not only on the original Heston model, but also on the many enhancements and refinements that have been applied to the model, including methods that use the Fourier transform, numerical integration schemes, simulation, methods for pricing American options, and much more. The companion website offers pricing code in VBA that resides in an extensive set of Excel spreadsheets. The Heston model is the derivatives industry's most popular stochastic volatility model for pricing equity derivatives. This book provides complete guidance toward the successful implementation of this valuable model using the industry's ubiquitous financial modeling software, giving users the understanding—and VBA code—they need to produce option prices that are more accurate, and volatility surfaces that more closely reflect market conditions. Derivatives pricing is often the hinge on which profit is made or lost in financial institutions, making accuracy of utmost importance. This book will help risk managers, traders, portfolio managers, quants, academics and other professionals better understand the Heston model and its extensions, in a writing style that is clear, concise, transparent and easy to understand. For better pricing accuracy, The Heston Model and Its Extensions in VBA is a crucial resource for producing more accurate model outputs such as prices, hedge ratios, volatilities, and graphs.
Financial Modelling
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Author : Joerg Kienitz
language : en
Publisher: John Wiley & Sons
Release Date : 2012-09-10
Financial Modelling written by Joerg Kienitz and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-10 with Business & Economics categories.
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.
Handbook Of Volatility Models And Their Applications
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Author : Luc Bauwens
language : en
Publisher: John Wiley & Sons
Release Date : 2012-03-22
Handbook Of Volatility Models And Their Applications written by Luc Bauwens and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-22 with Business & Economics categories.
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.
The Heston Model And Its Extensions In Matlab And C
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Author : Fabrice D. Rouah
language : en
Publisher: John Wiley & Sons
Release Date : 2013-08-01
The Heston Model And Its Extensions In Matlab And C written by Fabrice D. Rouah and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-01 with Business & Economics categories.
Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.
Monte Carlo Methods And Models In Finance And Insurance
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Author : Ralf Korn
language : en
Publisher: CRC Press
Release Date : 2010-02-26
Monte Carlo Methods And Models In Finance And Insurance written by Ralf Korn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-26 with Business & Economics categories.
Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Rom