Interest Rate Models An Infinite Dimensional Stochastic Analysis Perspective
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Interest Rate Models An Infinite Dimensional Stochastic Analysis Perspective
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Author : René Carmona
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-22
Interest Rate Models An Infinite Dimensional Stochastic Analysis Perspective written by René Carmona 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 2007-05-22 with Mathematics categories.
This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution equations in infinite dimensions. The text includes a crash course on interest rates, a self-contained introduction to infinite dimensional stochastic analysis, and recent results in interest rate theory. From the reviews: "A wonderful book. The authors present some cutting-edge math." --WWW.RISKBOOK.COM
Infinite Dimensional Stochastic Analysis
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Author : Hui-Hsiung Kuo
language : en
Publisher: World Scientific
Release Date : 2008
Infinite Dimensional Stochastic Analysis written by Hui-Hsiung Kuo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
An Elementary Introduction To Stochastic Interest Rate Modeling
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Author : Nicolas Privault
language : en
Publisher: World Scientific
Release Date : 2012
An Elementary Introduction To Stochastic Interest Rate Modeling written by Nicolas Privault and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Business & Economics categories.
Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students. This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises with their solutions, and a new introductory chapter on credit risk. The stochastic interest rate models considered range from standard short rate to forward rate models, with a treatment of the pricing of related derivatives such as caps and swaptions under forward measures. Some more advanced topics including the BGM model and an approach to its calibration are also covered.
Stochastic Models For Prices Dynamics In Energy And Commodity Markets
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Author : Fred Espen Benth
language : en
Publisher: Springer Nature
Release Date : 2023-11-16
Stochastic Models For Prices Dynamics In Energy And Commodity Markets written by Fred Espen Benth and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-16 with Mathematics categories.
This monograph presents a theory for random field models in time and space, viewed as stochastic processes with values in a Hilbert space, to model the stochastic dynamics of forward and futures prices in energy, power, and commodity markets. In this book, the well-known Heath–Jarrow–Morton approach from interest rate theory is adopted and extended into an infinite-dimensional framework, allowing for flexible modeling of price stochasticity across time and along the term structure curve. Various models are introduced based on stochastic partial differential equations with infinite-dimensional Lévy processes as noise drivers, emphasizing random fields described by low-dimensional parametric covariance functions instead of classical high-dimensional factor models. The Filipović space, a separable Hilbert space of Sobolev type, is found to be a convenient state space for the dynamics of forward and futures term structures. The monograph provides a classification of important operators in this space, covering covariance operators and the stochastic modeling of volatility term structures, including the Samuelson effect. Fourier methods are employed to price many derivatives of interest in energy, power, and commodity markets, and sensitivity 'delta' expressions can be derived. Additionally, the monograph covers forward curve smoothing, the connection between forwards with fixed delivery and delivery period, as well as the classical theory of forward and futures pricing. This monograph will appeal to researchers and graduate students interested in mathematical finance and stochastic analysis applied in the challenging markets of energy, power, and commodities. Practitioners seeking sophisticated yet flexible and analytically tractable risk models will also find it valuable.
Elementary Introduction To Stochastic Interest Rate Modeling An 2nd Edition
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Author : Nicolas Privault
language : en
Publisher: World Scientific
Release Date : 2012-05-04
Elementary Introduction To Stochastic Interest Rate Modeling An 2nd Edition written by Nicolas Privault and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.
Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students.This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises with their solutions, and a new introductory chapter on credit risk. The stochastic interest rate models considered range from standard short rate to forward rate models, with a treatment of the pricing of related derivatives such as caps and swaptions under forward measures. Some more advanced topics including the BGM model and an approach to its calibration are also covered.
Stochastic Cauchy Problems In Infinite Dimensions
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Author : Irina V. Melnikova
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Stochastic Cauchy Problems In Infinite Dimensions written by Irina V. Melnikova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
Interest Rate Models Theory And Practice
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Author : Damiano Brigo
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-26
Interest Rate Models Theory And Practice written by Damiano Brigo 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 2007-09-26 with Mathematics categories.
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.
Mathematics Of The Bond Market A L Vy Processes Approach
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Author : Michał Barski
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23
Mathematics Of The Bond Market A L Vy Processes Approach written by Michał Barski 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 2020-04-23 with Business & Economics categories.
Analyses bond market models with Lévy stochastic factors, suitable for graduates and researchers in probability and mathematical finance.
Modeling The Term Structure Of Interest Rates
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Author : Rajna Gibson
language : en
Publisher: Now Publishers Inc
Release Date : 2010
Modeling The Term Structure Of Interest Rates written by Rajna Gibson and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Business & Economics categories.
Modeling the Term Structure of Interest Rates provides a comprehensive review of the continuous-time modeling techniques of the term structure applicable to value and hedge default-free bonds and other interest rate derivatives.
New Methods In Fixed Income Modeling
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Author : Mehdi Mili
language : en
Publisher: Springer
Release Date : 2018-08-18
New Methods In Fixed Income Modeling written by Mehdi Mili and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-18 with Business & Economics categories.
This book presents new approaches to fixed income modeling and portfolio management techniques. Taking into account the latest mathematical and econometric developments in finance, it analyzes the hedging securities and structured instruments that are offered by banks, since recent research in the field of fixed incomes and financial markets has raised awareness for changes in market risk management strategies. The book offers a valuable resource for all researchers and practitioners interested in the theory behind fixed income instruments, and in their applications in financial portfolio management.