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| an elementary introduction to stochastic interest rate modeling: An Elementary Introduction to Stochastic Interest Rate Modeling Nicolas Privault, 2008 This textbook is written as an accessible introduction to interest rate modeling and related derivatives, which have become increasingly important subjects of interest in financial mathematics. The models considered range from standard short rate to forward rate models and include more advanced topics such as the BGM model and an approach to its calibration. An elementary treatment of the pricing of caps and swaptions under forward measures is also provided, with a focus on explicit calculations and a step-by-step introduction of concepts. Each chapter is accompanied with exercises and their complete solutions, making this book suitable for advanced undergraduate or beginning graduate-level students. |
| an elementary introduction to stochastic interest rate modeling: An Elementary Introduction to Stochastic Interest Rate Modeling Nicolas Privault, 2012 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. |
| an elementary introduction to stochastic interest rate modeling: Elementary Introduction To Stochastic Interest Rate Modeling, An (2nd Edition) Nicolas Privault, 2012-05-04 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. |
| an elementary introduction to stochastic interest rate modeling: Stochastic Interest Rate Modeling With Fixed Income Derivative Pricing (Third Edition) Nicolas Privault, 2021-09-02 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. |
| an elementary introduction to stochastic interest rate modeling: An Introduction to Stochastic Modeling Howard M. Taylor, Samuel Karlin, 2014-05-10 An Introduction to Stochastic Modeling, Revised Edition 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. |
| an elementary introduction to stochastic interest rate modeling: Modeling the Term Structure of Interest Rates Rajna Gibson, François-Serge Lhabitant, Denis Talay, 2010 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. |
| an elementary introduction to stochastic interest rate modeling: Stochastic Models of Financial Mathematics Vigirdas Mackevicius, 2016-11-08 This book presents a short introduction to continuous-time financial models. An overview of the basics of stochastic analysis precedes a focus on the Black–Scholes and interest rate models. Other topics covered include self-financing strategies, option pricing, exotic options and risk-neutral probabilities. Vasicek, Cox-Ingersoll-Ross, and Heath–Jarrow–Morton interest rate models are also explored. The author presents practitioners with a basic introduction, with more rigorous information provided for mathematicians. The reader is assumed to be familiar with the basics of probability theory. Some basic knowledge of stochastic integration and differential equations theory is preferable, although all preliminary information is given in the first part of the book. Some relatively simple theoretical exercises are also provided. - About continuous-time stochastic models of financial mathematics - Black-Sholes model and interest rate models - Requiring a minimum knowledge of stochastic integration and stochastic differential equations |
| an elementary introduction to stochastic interest rate modeling: Analysis for Diffusion Processes on Riemannian Manifolds Feng-Yu Wang, 2014 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. |
| an elementary introduction to stochastic interest rate modeling: Risk-sensitive Investment Management Mark H A Davis, Sebastien Lleo, 2014-07-21 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. |
| an elementary introduction to stochastic interest rate modeling: Change Of Time And Change Of Measure (Second Edition) Ole E Barndorff-nielsen, Albert N Shiryaev, 2015-05-07 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'. |
| an elementary introduction to stochastic interest rate modeling: Spatial Branching In Random Environments And With Interaction Janos Englander, 2014-11-20 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. |
| an elementary introduction to stochastic interest rate modeling: Stochastic Processes, Finance and Control Samuel N. Cohen, 2012 This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy. |
| an elementary introduction to stochastic interest rate modeling: Implicit Embedded Options in Life Insurance Contracts Nils Rüfenacht, 2012-04-03 This book presents a market-consistent valuation framework for implicit embedded options in life insurance contracts. This framework is used to perform an empirical analysis based on more than 110,000 actual and in-force life insurance policies and with a focus on the modeling of interest rates. Its results are the answer to the central question posed in the objectives: What value do the embedded options and guarantees considered have? This question is answered both absolutely and relative to the current policy reserves, from the perspective of the insurer, the policyholder and the shareholder respectively |
| an elementary introduction to stochastic interest rate modeling: Ruin Probabilities (2nd Edition) Soren Asmussen, Hansjorg Albrecher, 2010-09-09 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 elementary introduction to stochastic interest rate modeling: Hedging Derivatives Thorsten Rheinlander, Jenny Sexton, 2011 Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This volume provides a systematic treatment of hedging in incomplete markets. Mean-variance hedging under the risk-neutral measure is applied in the framework of exponential L(r)vy processes and for derivatives written on defaultable assets. It is discussed how to complete markets based upon stochastic volatility models via trading in both stocks and vanilla options. Exponential utility indifference pricing is explored via a duality with entropy minimization. Backward stochastic differential equations offer an alternative approach and are moreover applied to study markets with trading constraints including basis risk. A range of optimal martingale measures are discussed including the entropy, Esscher and minimal martingale measures. Quasi-symmetry properties of stochastic processes are deployed in the semi-static hedging of barrier options. This book is directed towards both graduate students and researchers in mathematical finance, and will also provide an orientation to applied mathematicians, financial economists and practitioners wishing to explore recent progress in this field. |
| an elementary introduction to stochastic interest rate modeling: An Introduction to the Mathematics of Finance Stephen Garrett, 2013-05-28 An Introduction to the Mathematics of Finance: A Deterministic Approach, Second edition, offers a highly illustrated introduction to mathematical finance, with a special emphasis on interest rates. This revision of the McCutcheon-Scott classic follows the core subjects covered by the first professional exam required of UK actuaries, the CT1 exam. It realigns the table of contents with the CT1 exam and includes sample questions from past exams of both The Actuarial Profession and the CFA Institute. With a wealth of solved problems and interesting applications, An Introduction to the Mathematics of Finance stands alone in its ability to address the needs of its primary target audience, the actuarial student. - Closely follows the syllabus for the CT1 exam of The Institute and Faculty of Actuaries - Features new content and more examples - Online supplements available: http://booksite.elsevier.com/9780080982403/ - Includes past exam questions from The Institute and Faculty of Actuaries and the CFA Institute |
| an elementary introduction to stochastic interest rate modeling: Pseudo-Regularly Varying Functions and Generalized Renewal Processes Valeriĭ V. Buldygin, Karl-Heinz Indlekofer, Oleg I. Klesov, Josef G. Steinebach, 2018-10-12 One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors’ research work and approach – first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory. |
| an elementary introduction to stochastic interest rate modeling: Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective René Carmona, M R Tehranchi, 2007-05-22 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 |
| an elementary introduction to stochastic interest rate modeling: Term-Structure Models Damir Filipovic, 2009-07-28 Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis. |
| an elementary introduction to stochastic interest rate modeling: Martingale Methods in Financial Modelling Marek Musiela, 2013-06-29 The origin of this book can be traced to courses on financial mathemat ics taught by us at the University of New South Wales in Sydney, Warsaw University of Technology (Politechnika Warszawska) and Institut National Polytechnique de Grenoble. Our initial aim was to write a short text around the material used in two one-semester graduate courses attended by students with diverse disciplinary backgrounds (mathematics, physics, computer sci ence, engineering, economics and commerce). The anticipated diversity of potential readers explains the somewhat unusual way in which the book is written. It starts at a very elementary mathematical level and does not as sume any prior knowledge of financial markets. Later, it develops into a text which requires some familiarity with concepts of stochastic calculus (the basic relevant notions and results are collected in the appendix). Over time, what was meant to be a short text acquired a life of its own and started to grow. The final version can be used as a textbook for three one-semester courses one at undergraduate level, the other two as graduate courses. The first part of the book deals with the more classical concepts and results of arbitrage pricing theory, developed over the last thirty years and currently widely applied in financial markets. The second part, devoted to interest rate modelling is more subjective and thus less standard. A concise survey of short-term interest rate models is presented. However, the special emphasis is put on recently developed models built upon market interest rates. |
| an elementary introduction to stochastic interest rate modeling: Data Science and Risk Analytics in Finance and Insurance Tze Leung Lai, Haipeng Xing, 2024-10-02 This book presents statistics and data science methods for risk analytics in quantitative finance and insurance. Part I covers the background, financial models, and data analytical methods for market risk, credit risk, and operational risk in financial instruments, as well as models of risk premium and insolvency in insurance contracts. Part II provides an overview of machine learning (including supervised, unsupervised, and reinforcement learning), Monte Carlo simulation, and sequential analysis techniques for risk analytics. In Part III, the book offers a non-technical introduction to four key areas in financial technology: artificial intelligence, blockchain, cloud computing, and big data analytics. Key Features: Provides a comprehensive and in-depth overview of data science methods for financial and insurance risks. Unravels bandits, Markov decision processes, reinforcement learning, and their interconnections. Promotes sequential surveillance and predictive analytics for abrupt changes in risk factors. Introduces the ABCDs of FinTech: Artificial intelligence, blockchain, cloud computing, and big data analytics. Includes supplements and exercises to facilitate deeper comprehension. |
| an elementary introduction to stochastic interest rate modeling: Essentials Of Stochastic Finance: Facts, Models, Theory Albert N Shiryaev, 1999-01-15 This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks. |
| an elementary introduction to stochastic interest rate modeling: Brownian Motion Calculus Ubbo F. Wiersema, 2008-08-06 Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website. |
| an elementary introduction to stochastic interest rate modeling: Interest Rate Models - Theory and Practice Damiano Brigo, Fabio Mercurio, 2007-09-26 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. |
| an elementary introduction to stochastic interest rate modeling: Stochastic Simulation and Applications in Finance with MATLAB Programs Huu Tue Huynh, Van Son Lai, Issouf Soumare, 2011-11-21 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. |
| an elementary introduction to stochastic interest rate modeling: Consistency Problems for Heath-Jarrow-Morton Interest Rate Models Damir Filipovic, 2004-11-02 Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up to a finite number of trade assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinite-dimensional variable which is not directly observable. On the empirical side, this necessitates curve-fitting methods for the daily estimation of the term structure. Pricing models, on the other hand, are usually built upon stochastic factors representing the term structure in a finite-dimensional state space. Written for readers with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, this research monograph has threefold aims: to bring together estimation methods and factor models for interest rates, to provide appropriate consistency conditions and to explore some important examples. |
| an elementary introduction to stochastic interest rate modeling: Stochastic Finance Nicolas Privault, 2013-12-20 Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including Black–Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading. With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics. |
| an elementary introduction to stochastic interest rate modeling: Introduction To Stochastic Calculus With Applications (2nd Edition) Fima C Klebaner, 2005-06-20 This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author./a |
| an elementary introduction to stochastic interest rate modeling: Stochastic Processes and Calculus Uwe Hassler, 2015-12-12 This textbook gives a comprehensive introduction to stochastic processes and calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over the past decades stochastic calculus and processes have gained great importance, because they play a decisive role in the modeling of financial markets and as a basis for modern time series econometrics. Mathematical theory is applied to solve stochastic differential equations and to derive limiting results for statistical inference on nonstationary processes. This introduction is elementary and rigorous at the same time. On the one hand it gives a basic and illustrative presentation of the relevant topics without using many technical derivations. On the other hand many of the procedures are presented at a technically advanced level: for a thorough understanding, they are to be proven. In order to meet both requirements jointly, the present book is equipped with a lot of challenging problems at the end of each chapter as well as with the corresponding detailed solutions. Thus the virtual text - augmented with more than 60 basic examples and 40 illustrative figures - is rather easy to read while a part of the technical arguments is transferred to the exercise problems and their solutions. |
| an elementary introduction to stochastic interest rate modeling: Computational Methods for Quantitative Finance Norbert Hilber, Oleg Reichmann, Christoph Schwab, Christoph Winter, 2013-02-15 Many mathematical assumptions on which classical derivative pricing methods are based have come under scrutiny in recent years. The present volume offers an introduction to deterministic algorithms for the fast and accurate pricing of derivative contracts in modern finance. This unified, non-Monte-Carlo computational pricing methodology is capable of handling rather general classes of stochastic market models with jumps, including, in particular, all currently used Lévy and stochastic volatility models. It allows us e.g. to quantify model risk in computed prices on plain vanilla, as well as on various types of exotic contracts. The algorithms are developed in classical Black-Scholes markets, and then extended to market models based on multiscale stochastic volatility, to Lévy, additive and certain classes of Feller processes. This book is intended for graduate students and researchers, as well as for practitioners in the fields of quantitative finance and applied and computational mathematics with a solid background in mathematics, statistics or economics. |
| an elementary introduction to stochastic interest rate modeling: An Introduction to Mathematical Modeling Edward A. Bender, 2012-05-23 Employing a practical, learn by doing approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications. |
| an elementary introduction to stochastic interest rate modeling: Derivatives Jiří Witzany, 2020-11-04 This book helps students, researchers and quantitative finance practitioners to understand both basic and advanced topics in the valuation and modeling of financial and commodity derivatives, their institutional framework and risk management. It provides an overview of the new regulatory requirements such as Basel III, the Fundamental Review of the Trading Book (FRTB), Interest Rate Risk of the Banking Book (IRRBB), or the Internal Capital Assessment Process (ICAAP). The reader will also find a detailed treatment of counterparty credit risk, stochastic volatility estimation methods such as MCMC and Particle Filters, and the concepts of model-free volatility, VIX index definition and the related volatility trading. The book can also be used as a teaching material for university derivatives and financial engineering courses. |
| an elementary introduction to stochastic interest rate modeling: Interest Rate Modeling Lixin Wu, 2009-05-14 Containing many results that are new or exist only in recent research articles, Interest Rate Modeling: Theory and Practice portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale app |
| an elementary introduction to stochastic interest rate modeling: Handbook in Monte Carlo Simulation Paolo Brandimarte, 2014-06-20 An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation. |
| an elementary introduction to stochastic interest rate modeling: An Introduction to the Geometry of Stochastic Flows Fabrice Baudoin, 2004 This book aims to provide a self-contained introduction to the local geometry of the stochastic flows. It studies the hypoelliptic operators, which are written in HArmanderOCOs form, by using the connection between stochastic flows and partial differential equations. The book stresses the authorOCOs view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry, and its main tools are introduced throughout the text. |
| an elementary introduction to stochastic interest rate modeling: Advances in Computer and Information Sciences and Engineering Tarek Sobh, 2008-08-15 Advances in Computer and Information Sciences and Engineering includes a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of Computer Science, Software Engineering, Computer Engineering, and Systems Engineering and Sciences. Advances in Computer and Information Sciences and Engineering includes selected papers from the conference proceedings of the International Conference on Systems, Computing Sciences and Software Engineering (SCSS 2007) which was part of the International Joint Conferences on Computer, Information and Systems Sciences and Engineering (CISSE 2007). |
| an elementary introduction to stochastic interest rate modeling: Financial Calculus Martin Baxter, Andrew Rennie, 1996-09-19 A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities. |
| an elementary introduction to stochastic interest rate modeling: Efficient Methods for Valuing Interest Rate Derivatives Antoon Pelsser, 2000-07-31 This book provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore a host of practical issues. |
| an elementary introduction to stochastic interest rate modeling: Understanding Markov Chains Nicolas Privault, 2013-08-13 This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions. |
| an elementary introduction to stochastic interest rate modeling: Modeling and Pricing in Financial Markets for Weather Derivatives Fred Espen Benth, Jurate Saltyte Benth, 2013 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 are 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. |
Elementary (TV Series 2012–2019) - IMDb
Elementary: Created by Robert Doherty. With Jonny Lee Miller, Lucy Liu, Aidan Quinn, Jon Michael Hill. A crime-solving duo that cracks the NYPD's most impossible cases. Following his …
Elementary (TV Series 2012–2019) - Episode list - IMDb
Holmes is excited to be consulted about the latest strike of 'balloon man', a serial killer who focuses on children. Analyzing the crime scene, Holmes' deductions lead to the recovery of …
"Elementary" The Long Fuse (TV Episode 2012) - IMDb
Nov 29, 2012 · The Long Fuse: Directed by Andrew Bernstein. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. While Watson struggles with Holmes over finding a new …
"Elementary" Pilot (TV Episode 2012) - IMDb
Sep 27, 2012 · Pilot: Directed by Michael Cuesta. With Jonny Lee Miller, Lucy Liu, Aidan Quinn, Dallas Roberts. Sherlock Holmes, fresh out of rehab, is teamed with a sobriety partner, a …
"Elementary" Be My Guest (TV Episode 2017) - IMDb
Jan 8, 2017 · Be My Guest: Directed by Maja Vrvilo. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Nelsan Ellis. Holmes and Watson race to find a woman who's been held captive for years …
"Elementary" Flight Risk (TV Episode 2012) - IMDb
Nov 8, 2012 · Flight Risk: Directed by David Platt. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. After a small jet crashes killing four people, Holmes battles both the police …
Abbott Elementary (TV Series 2021– ) - Episode list - IMDb
Janine prepares to meet her student's mother during open house, while the rest of the faculty uses the time to relax; Gregory is taken aback when he learns how Ava got the principal job; …
"Elementary" The Deductionist (TV Episode 2013) - IMDb
Feb 3, 2013 · The Deductionist: Directed by John Polson. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. A convicted killer who is supposed to donate a kidney to his sister …
"Elementary" A Stitch in Time (TV Episode 2015) - IMDb
Apr 16, 2015 · A Stitch in Time: Directed by Ron Fortunato. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. Holmes and Watson investigate the murder of a professional …
"Elementary" Just a Regular Irregular (TV Episode 2014) - IMDb
Nov 13, 2014 · Just a Regular Irregular: Directed by Jerry Levine. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. Sherlock helps a math genius from his network of "Irregulars" …
Elementary (TV Series 2012–2019) - IMDb
Elementary: Created by Robert Doherty. With Jonny Lee Miller, Lucy Liu, Aidan Quinn, Jon Michael Hill. A crime-solving duo that cracks the NYPD's most impossible cases. Following his …
Elementary (TV Series 2012–2019) - Episode list - IMDb
Holmes is excited to be consulted about the latest strike of 'balloon man', a serial killer who focuses on children. Analyzing the crime scene, Holmes' deductions lead to the recovery of …
"Elementary" The Long Fuse (TV Episode 2012) - IMDb
Nov 29, 2012 · The Long Fuse: Directed by Andrew Bernstein. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. While Watson struggles with Holmes over finding a new …
"Elementary" Pilot (TV Episode 2012) - IMDb
Sep 27, 2012 · Pilot: Directed by Michael Cuesta. With Jonny Lee Miller, Lucy Liu, Aidan Quinn, Dallas Roberts. Sherlock Holmes, fresh out of rehab, is teamed with a sobriety partner, a …
"Elementary" Be My Guest (TV Episode 2017) - IMDb
Jan 8, 2017 · Be My Guest: Directed by Maja Vrvilo. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Nelsan Ellis. Holmes and Watson race to find a woman who's been held captive for years …
"Elementary" Flight Risk (TV Episode 2012) - IMDb
Nov 8, 2012 · Flight Risk: Directed by David Platt. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. After a small jet crashes killing four people, Holmes battles both the police …
Abbott Elementary (TV Series 2021– ) - Episode list - IMDb
Janine prepares to meet her student's mother during open house, while the rest of the faculty uses the time to relax; Gregory is taken aback when he learns how Ava got the principal job; …
"Elementary" The Deductionist (TV Episode 2013) - IMDb
Feb 3, 2013 · The Deductionist: Directed by John Polson. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. A convicted killer who is supposed to donate a kidney to his sister …
"Elementary" A Stitch in Time (TV Episode 2015) - IMDb
Apr 16, 2015 · A Stitch in Time: Directed by Ron Fortunato. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. Holmes and Watson investigate the murder of a professional …
"Elementary" Just a Regular Irregular (TV Episode 2014) - IMDb
Nov 13, 2014 · Just a Regular Irregular: Directed by Jerry Levine. With Jonny Lee Miller, Lucy Liu, Jon Michael Hill, Aidan Quinn. Sherlock helps a math genius from his network of "Irregulars" …
