An Elementary Introduction to Stochastic Interest Rate Modeling
An Elementary Introduction to Stochastic Interest Rate Modeling

Author: Nicolas Privault

Publisher: World Scientific

Published: 2012

Total Pages: 243

ISBN-13: 9814390860

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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.

Elementary Introduction To Stochastic Interest Rate Modeling, An (2nd Edition)
Elementary Introduction To Stochastic Interest Rate Modeling, An (2nd Edition)

Author: Nicolas Privault

Publisher: World Scientific

Published: 2012-05-04

Total Pages: 243

ISBN-13: 9814401641

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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 Interest Rate Modeling With Fixed Income Derivative Pricing (Third Edition)
Stochastic Interest Rate Modeling With Fixed Income Derivative Pricing (Third Edition)

Author: Nicolas Privault

Publisher: World Scientific

Published: 2021-09-02

Total Pages: 373

ISBN-13: 9811226628

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This book introduces the mathematics of stochastic interest rate modeling and the pricing of related derivatives, based on a step-by-step presentation of concepts with a focus on explicit calculations. The types of interest rates considered range from short rates to forward rates such as LIBOR and swap rates, which are presented in the HJM and BGM frameworks. The pricing and hedging of interest rate and fixed income derivatives such as bond options, caps, and swaptions, are treated using forward measure techniques. An introduction to default bond pricing and an outlook on model calibration are also included as additional topics.This third edition represents a significant update on the second edition published by World Scientific in 2012. Most chapters have been reorganized and largely rewritten with additional details and supplementary solved exercises. New graphs and simulations based on market data have been included, together with the corresponding R codes.This new edition also contains 75 exercises and 4 problems with detailed solutions, making it suitable for advanced undergraduate and graduate level students.

Change Of Time And Change Of Measure (Second Edition)
Change Of Time And Change Of Measure (Second Edition)

Author: Ole E Barndorff-nielsen

Publisher: World Scientific Publishing Company

Published: 2015-05-07

Total Pages: 345

ISBN-13: 9814678600

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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'.

Modeling and Pricing in Financial Markets for Weather Derivatives
Modeling and Pricing in Financial Markets for Weather Derivatives

Author: Fred Espen Benth

Publisher: World Scientific

Published: 2013

Total Pages: 255

ISBN-13: 9814401854

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Weather derivatives provide a tool for weather risk management, and the markets for these exotic financial products are gradually emerging in size and importance. This unique monograph presents a unified approach to the modeling and analysis of such weather derivatives, including financial contracts on temperature, wind and rain. Based on a deep statistical analysis of weather factors, sophisticated stochastic processes are introduced modeling the time and space dynamics. Applying ideas from the modern theory of mathematical finance, weather derivatives are priced, and questions of hedging analyzed. The treatise contains an in-depth analysis of typical weather contracts traded at the Chicago Mercantile Exchange (CME), including so-called CDD and HDD futures. The statistical analysis of weather variables is based on a large data set from Lithuania.The monograph includes the research done by the authors over the last decade on weather markets. Their work has gained considerable attention, and has been applied in many contexts.

Analysis for Diffusion Processes on Riemannian Manifolds
Analysis for Diffusion Processes on Riemannian Manifolds

Author: Feng-Yu Wang

Publisher: World Scientific

Published: 2014

Total Pages: 392

ISBN-13: 9814452653

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Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

Risk-sensitive Investment Management
Risk-sensitive Investment Management

Author: Mark H A Davis

Publisher: World Scientific

Published: 2014-07-21

Total Pages: 414

ISBN-13: 9814578061

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Over the last two decades, risk-sensitive control has evolved into an innovative and successful framework for solving dynamically a wide range of practical investment management problems.This book shows how to use risk-sensitive investment management to manage portfolios against an investment benchmark, with constraints, and with assets and liabilities. It also addresses model implementation issues in parameter estimation and numerical methods. Most importantly, it shows how to integrate jump-diffusion processes which are crucial to model market crashes.With its emphasis on the interconnection between mathematical techniques and real-world problems, this book will be of interest to both academic researchers and money managers. Risk-sensitive investment management links stochastic control and portfolio management. Because of its distinct emphasis on integrating advanced theoretical concepts into practical dynamic investment management tools, this book stands out from the existing literature in fundamental ways. It goes beyond mainstream research in portfolio management in a traditional static setting. The theoretical developments build on contemporary research in stochastic control theory, but are informed throughout by the need to construct an effective and practical framework for dynamic portfolio management.This book fills a gap in the literature by connecting mathematical techniques with the real world of investment management. Readers seeking to solve key problems such as benchmarked asset management or asset and liability management will certainly find it useful.

Spatial Branching In Random Environments And With Interaction
Spatial Branching In Random Environments And With Interaction

Author: Janos Englander

Publisher: World Scientific

Published: 2014-11-20

Total Pages: 286

ISBN-13: 9814569852

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This unique volume discusses some recent developments in the theory of spatial branching processes and superprocesses, with special emphasis on spines, Laws of Large Numbers, interactions and random media.Although this book is mainly written for mathematicians, the models discussed are relevant to certain models in population biology, and are thus hopefully interesting to the applied mathematician/biologist as well.The necessary background material in probability and analysis is provided in a comprehensive introductory chapter. Historical notes and several exercises are provided to complement each chapter.

Ruin Probabilities (2nd Edition)
Ruin Probabilities (2nd Edition)

Author: Soren Asmussen

Publisher: World Scientific

Published: 2010-09-09

Total Pages: 621

ISBN-13: 9814466921

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The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.

An Introduction to Stochastic Modeling
An Introduction to Stochastic Modeling

Author: Howard M. Taylor

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 410

ISBN-13: 1483269272

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An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.