On Term Structure Of Yield Rates 3 The Duffie Kan One Factor Model

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On Term Structure of Yield Rates. 3. The Duffie - Kan One-Factor Model

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 3. The Duffie - Kan One-Factor Model by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 3. The Duffie - Kan One-Factor Model written by Gennady Medvedev and published by . This book was released on 2017 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The time structure of interest rates plays a key role at the bond pricing. Therefore its properties interest many financial analysts. However in the available literature usually there is a schematic description of these properties. Attempt of the detailed description of all possible forms of time structure for a class of affine models of interest rates as for these models it is possible to write down decisions in the closed form here becomes. As the basic the model of Duffie - Kan (DK) with any bottom border for risk free (spot) interest rate is accepted. Results for widely known models CIR and Vasiček turn out as special cases. For one-factor model of affine yield of Duffie - Kan analytical representations of yield curves and forward curves are found and their properties when the duration measure of risk free rates as a time variable is used are investigated. It is shown that for all variety of parameters exist only four possible kinds of yield curves. For small terms to maturity a bond yield is defined, basically, current level of risk free rates while for very long terms to maturity the yield is defined by a stationary expectation of risk free rates. In this connection it would be possible to expect that influence of current level of risk free rates on yield with time increase will damp. However, it is not so. It has appeared that current level of risk free rates essentially influences on sight of entire yield curve and a forward curve. Let's notice also that yield curve and a forward curve start from one point and at increase in term to maturity converge to the same limit that differs from usually accepted point of view that these curves diverge when the term to maturity increase.

On Term Structure of Yield Rates. 4. The Duffie - Kan Two Factor Model

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 4. The Duffie - Kan Two Factor Model by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 4. The Duffie - Kan Two Factor Model written by Gennady Medvedev and published by . This book was released on 2017 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate models in which the short-term rate is a unique state variable are usually considered. These models are attractive that analytical decisions often give the chance to receive and provide concerning the simple computing analysis. However one-factor models have certain lacks. Basic of them consists that all term structure determines by only the unique value of the short-term rate fixed at the initial moment of construction of term structure. And it is represented unreasonable from the economic point of view. To avoid this lack authors suggest to use for modeling of dynamics of the interest rate more than one state variable. At transition from the unique factor to several there should be an improvement of approximation of term structure. In general the price for it is loss of possibility of receiving of analytical decisions, receiving of the equations with partial derivatives with the raised dimension and complication of procedure of receiving of results. In the paper the Duffie-Kan models, describing dynamics of the short-term interest rate in a case when the state of the financial market is characterized not only by level of the interest rate, but also one more other parameter changing in time are investigated. It is considered two cases. In the first in quality of an additional state variable local on time the average value of the short-term interest rate is accepted. In the second case as an additional state variable the instant variance of the interest rate is accepted. Two-factor models are under construction so that they led to affine term structure of yield. The basic attention is given to definition of functions of term structure. As the equations turning out for these functions do not suppose analytical decisions, it is offered to find their approximations. In view of that in real cases the volatility is usually small, the method of small parameter of Poincare is for this purpose used.

On Term Structure of Yield Rates. 6. The Three Factor Model

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 6. The Three Factor Model by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 6. The Three Factor Model written by Gennady Medvedev and published by . This book was released on 2017 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models of Duffie - Kan, d ...

On Term Structure of Yield Rates. 5. The Duffie - Kan Two Factor Model (Continuation).

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 5. The Duffie - Kan Two Factor Model (Continuation). by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 5. The Duffie - Kan Two Factor Model (Continuation). written by Gennady Medvedev and published by . This book was released on 2017 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models of Daffie-Kan, describing dynamics of a short-term interest rate in a case when the state of the financial market is characterized not only by level of the interest rate, but also one more parameter changing in time are investigated. Two cases are considered. In the first in quality of an additional state variable the local on time average value of a short-term interest rate is taken. In the second case as an additional state variable the instant variance of an interest rate is accepted. Two-factor models are under construction so that they led to affine term structure of yield. The main attention is given to properties of yield curve and a forward curve when dynamics of a short-term interest rate is described by two-factor models of Daffie-Kan. Because functions of term structure for additional variables in a closed form can't be received, the type of curves as a whole (for entire interval of change of time) is analyzed by means of numerical calculations though properties of curves on the ends of an interval become clear analytically. For model «a rate - its local average» it is appeared that limiting properties of long-term yield are defined only by properties of an additional variable - local average of interest rates. For model «a rate - its instant variance» it became clear that this model has economic sense only when the weight factor of instant variance at determination of a short-term yield rate is equal to zero. Comparison of yield curves and forward curves for one-factor model and two-factor models shows that at the accepted parameters these curves considerably differ. As values of weight factors essentially influence behavior of yield curves and forward curves, they should be estimated along with market parameters of the price of risk.

Modeling the Term Structure of Interest Rates

Author : Rajna Gibson
Publisher : Now Publishers Inc
ISBN 13 : 1601983727
Total Pages : 171 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Modeling the Term Structure of Interest Rates by : Rajna Gibson

Download or read book Modeling the Term Structure of Interest Rates written by Rajna Gibson and published by Now Publishers Inc. This book was released on 2010 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Yield-factor Model of Interest Rates

Author : Darrell Duffie
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (464 download)

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Book Synopsis A Yield-factor Model of Interest Rates by : Darrell Duffie

Download or read book A Yield-factor Model of Interest Rates written by Darrell Duffie and published by . This book was released on 1995 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On Term Structure of Yield Rates. 7. Another Temporal Variable for Maturities

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 7. Another Temporal Variable for Maturities by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 7. Another Temporal Variable for Maturities written by Gennady Medvedev and published by . This book was released on 2017 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In paper it is offered to consider a time variable that describes term to maturity of zero-coupon bonds as result of nonlinear transformation of the temporary terms that are independent on parameters of interest rate dynamics model, allowing to map the time numerical axis into an interval of unit length. This way has advantages before application as a measure of time of a duration of a short-term interest rate because at the duration application the time variable depends on parameters of considered models that complicates a comparison of yields for the same real terms to maturity. It is shown that resulting yield functions possess practically the same properties as a yield to maturity curve and a forward curve, except for (in certain cases) properties connected with the second derivative. At the same time they it is more convenient because allow to analyze visually the yields on all time axis. Use of such approach is illustrated in the analysis of properties of the yield curve and the forward curve for one-factor model of Duffie - Kan, Fong - Vasicek two-factor model and three-factor models of interest rates: Fong - Vasicek expanded model, Chen model and the BDFS model. In paper the mathematical models of dynamics of the state variables for all these cases (six various models) are formulated, the equations for functions of term structure are deduced and (when it is possible) their analytical solutions are found. As the main part of the equations can be solved only by calculations, numerical calculations for all six models are carried out and comparisons of yield functions characterizing their term structure are carried out. Calculations were carried out for a set of the parameters based on estimates, published by D. Ahn and B. Gao, fitting one-factor Duffie - Kan model for the description of dynamics of process of an annualized one-month U.S. Treasury bill rate for the supervision period from January, 1960 to February, 1991. Calculations showed that the increase of model dimension implies the decrease of yield rate.

Yield Curves and Forward Curves for Diffusion Models of Short Rates

Author : Gennady A. Medvedev
Publisher : Springer
ISBN 13 : 3030155005
Total Pages : 230 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Yield Curves and Forward Curves for Diffusion Models of Short Rates by : Gennady A. Medvedev

Download or read book Yield Curves and Forward Curves for Diffusion Models of Short Rates written by Gennady A. Medvedev and published by Springer. This book was released on 2019-05-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the study of the term structures of the yields of zero-coupon bonds. The methods it describes differ from those usually found in the literature in that the time variable is not the term to maturity but the interest rate duration, or another convenient non-linear transformation of terms. This makes it possible to consider yield curves not only for a limited interval of term values, but also for the entire positive semiaxis of terms. The main focus is the comparative analysis of yield curves and forward curves and the analytical study of their features. Generalizations of yield term structures are studied where the dimension of the state space of the financial market is increased. In cases where the analytical approach is too cumbersome, or impossible, numerical techniques are used. This book will be of interest to financial analysts, financial market researchers, graduate students and PhD students.

Yield Curve Modeling and Forecasting

Author : Francis X. Diebold
Publisher : Princeton University Press
ISBN 13 : 0691146802
Total Pages : 223 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Yield Curve Modeling and Forecasting by : Francis X. Diebold

Download or read book Yield Curve Modeling and Forecasting written by Francis X. Diebold and published by Princeton University Press. This book was released on 2013-01-15 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the dynamic evolution of the yield curve is critical to many financial tasks, including pricing financial assets and their derivatives, managing financial risk, allocating portfolios, structuring fiscal debt, conducting monetary policy, and valuing capital goods. Unfortunately, most yield curve models tend to be theoretically rigorous but empirically disappointing, or empirically successful but theoretically lacking. In this book, Francis Diebold and Glenn Rudebusch propose two extensions of the classic yield curve model of Nelson and Siegel that are both theoretically rigorous and empirically successful. The first extension is the dynamic Nelson-Siegel model (DNS), while the second takes this dynamic version and makes it arbitrage-free (AFNS). Diebold and Rudebusch show how these two models are just slightly different implementations of a single unified approach to dynamic yield curve modeling and forecasting. They emphasize both descriptive and efficient-markets aspects, they pay special attention to the links between the yield curve and macroeconomic fundamentals, and they show why DNS and AFNS are likely to remain of lasting appeal even as alternative arbitrage-free models are developed. Based on the Econometric and Tinbergen Institutes Lectures, Yield Curve Modeling and Forecasting contains essential tools with enhanced utility for academics, central banks, governments, and industry.

Term-Structure Models

Author : Damir Filipovic
Publisher : Springer Science & Business Media
ISBN 13 : 3540680152
Total Pages : 259 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Term-Structure Models by : Damir Filipovic

Download or read book Term-Structure Models written by Damir Filipovic and published by Springer Science & Business Media. This book was released on 2009-07-28 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theoretical and Empirical Analysis of Common Factors in a Term Structure Model

Author : Ting Ting Huang
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1443815829
Total Pages : 89 pages
Book Rating : 4.4/5 (438 download)

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Book Synopsis Theoretical and Empirical Analysis of Common Factors in a Term Structure Model by : Ting Ting Huang

Download or read book Theoretical and Empirical Analysis of Common Factors in a Term Structure Model written by Ting Ting Huang and published by Cambridge Scholars Publishing. This book was released on 2009-10-02 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is the first that completely studies dynamical and cross-sectional structures of bonds, typically used as risk-free assets in mathematical finance, on the independence of the common factors with the empirical copula. During the last decade, financial models based empirically on common factors have acquired increasing popularity in risk management and asset pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for non-specialists to understand, and the mathematical tools required for applications can be intimidating. Although many of the copula models used in finance are theoretical, the nature of financial data suggests the empirical copula is more appropriate for forecasting and accurately describing returns, volatility and interdependence.

Handbook of Fixed-Income Securities

Author : Pietro Veronesi
Publisher : John Wiley & Sons
ISBN 13 : 1118709187
Total Pages : 632 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Handbook of Fixed-Income Securities by : Pietro Veronesi

Download or read book Handbook of Fixed-Income Securities written by Pietro Veronesi and published by John Wiley & Sons. This book was released on 2016-03-23 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the current theories and methodologies intrinsic to fixed-income securities Written by well-known experts from a cross section of academia and finance, Handbook of Fixed-Income Securities features a compilation of the most up-to-date fixed-income securities techniques and methods. The book presents crucial topics of fixed income in an accessible and logical format. Emphasizing empirical research and real-life applications, the book explores a wide range of topics from the risk and return of fixed-income investments, to the impact of monetary policy on interest rates, to the post-crisis new regulatory landscape. Well organized to cover critical topics in fixed income, Handbook of Fixed-Income Securities is divided into eight main sections that feature: • An introduction to fixed-income markets such as Treasury bonds, inflation-protected securities, money markets, mortgage-backed securities, and the basic analytics that characterize them • Monetary policy and fixed-income markets, which highlight the recent empirical evidence on the central banks’ influence on interest rates, including the recent quantitative easing experiments • Interest rate risk measurement and management with a special focus on the most recent techniques and methodologies for asset-liability management under regulatory constraints • The predictability of bond returns with a critical discussion of the empirical evidence on time-varying bond risk premia, both in the United States and abroad, and their sources, such as liquidity and volatility • Advanced topics, with a focus on the most recent research on term structure models and econometrics, the dynamics of bond illiquidity, and the puzzling dynamics of stocks and bonds • Derivatives markets, including a detailed discussion of the new regulatory landscape after the financial crisis and an introduction to no-arbitrage derivatives pricing • Further topics on derivatives pricing that cover modern valuation techniques, such as Monte Carlo simulations, volatility surfaces, and no-arbitrage pricing with regulatory constraints • Corporate and sovereign bonds with a detailed discussion of the tools required to analyze default risk, the relevant empirical evidence, and a special focus on the recent sovereign crises A complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, Handbook of Fixed-Income Securities is also a useful supplementary textbook for graduate and MBA-level courses on fixed-income securities, risk management, volatility, bonds, derivatives, and financial markets. Pietro Veronesi, PhD, is Roman Family Professor of Finance at the University of Chicago Booth School of Business, where he teaches Masters and PhD-level courses in fixed income, risk management, and asset pricing. Published in leading academic journals and honored by numerous awards, his research focuses on stock and bond valuation, return predictability, bubbles and crashes, and the relation between asset prices and government policies.

Handbook of Quantitative Finance and Risk Management

Author : Cheng-Few Lee
Publisher : Springer Science & Business Media
ISBN 13 : 0387771174
Total Pages : 1700 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Handbook of Quantitative Finance and Risk Management by : Cheng-Few Lee

Download or read book Handbook of Quantitative Finance and Risk Management written by Cheng-Few Lee and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 1700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This two-volume handbook, comprised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.

Arbitrage Theory in Continuous Time

Author : Tomas Bjork
Publisher : Oxford University Press, USA
ISBN 13 : 0198851618
Total Pages : 584 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Arbitrage Theory in Continuous Time by : Tomas Bjork

Download or read book Arbitrage Theory in Continuous Time written by Tomas Bjork and published by Oxford University Press, USA. This book was released on 2020-01-16 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth edition of this widely used textbook on pricing and hedging of financial derivatives now also includes dynamic equilibrium theory and continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, Arbitrage Theory in Continuous Time is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Bjork has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. This edition includes an entirely new section presenting dynamic equilibrium theory, covering unit net supply endowments models and the Cox-Ingersoll-Ross equilibrium factor model. Providing two full treatments of arbitrage theory-the classical delta hedging approach and the modern martingale approach-this book is written so that these approaches can be studied independently of each other, thus providing the less mathematically-oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action. This textbook is a natural choice for graduate students and advanced undergraduates studying finance and an invaluable introduction to mathematical finance for mathematicians and professionals in the market.

Financial Economics and Econometrics

Author : Nikiforos T. Laopodis
Publisher : Taylor & Francis
ISBN 13 : 1000506053
Total Pages : 767 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Financial Economics and Econometrics by : Nikiforos T. Laopodis

Download or read book Financial Economics and Econometrics written by Nikiforos T. Laopodis and published by Taylor & Francis. This book was released on 2021-12-14 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial Economics and Econometrics provides an overview of the core topics in theoretical and empirical finance, with an emphasis on applications and interpreting results. Structured in five parts, the book covers financial data and univariate models; asset returns; interest rates, yields and spreads; volatility and correlation; and corporate finance and policy. Each chapter begins with a theory in financial economics, followed by econometric methodologies which have been used to explore the theory. Next, the chapter presents empirical evidence and discusses seminal papers on the topic. Boxes offer insights on how an idea can be applied to other disciplines such as management, marketing and medicine, showing the relevance of the material beyond finance. Readers are supported with plenty of worked examples and intuitive explanations throughout the book, while key takeaways, ‘test your knowledge’ and ‘test your intuition’ features at the end of each chapter also aid student learning. Digital supplements including PowerPoint slides, computer codes supplements, an Instructor’s Manual and Solutions Manual are available for instructors. This textbook is suitable for upper-level undergraduate and graduate courses on financial economics, financial econometrics, empirical finance and related quantitative areas.

Applied Quantitative Methods for Trading and Investment

Author : Christian L. Dunis
Publisher : John Wiley & Sons
ISBN 13 : 0470871342
Total Pages : 426 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Applied Quantitative Methods for Trading and Investment by : Christian L. Dunis

Download or read book Applied Quantitative Methods for Trading and Investment written by Christian L. Dunis and published by John Wiley & Sons. This book was released on 2004-01-09 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a manual on quantitative financial analysis. Focusing on advanced methods for modelling financial markets in the context of practical financial applications, it will cover data, software and techniques that will enable the reader to implement and interpret quantitative methodologies, specifically for trading and investment. Includes contributions from an international team of academics and quantitative asset managers from Morgan Stanley, Barclays Global Investors, ABN AMRO and Credit Suisse First Boston. Fills the gap for a book on applied quantitative investment & trading models Provides details of how to combine various models to manage and trade a portfolio

Risk and Financial Management

Author : Charles S. Tapiero
Publisher : John Wiley & Sons
ISBN 13 : 9780470849088
Total Pages : 364 pages
Book Rating : 4.8/5 (49 download)

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Book Synopsis Risk and Financial Management by : Charles S. Tapiero

Download or read book Risk and Financial Management written by Charles S. Tapiero and published by John Wiley & Sons. This book was released on 2004-04-23 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial risk management has become a popular practice amongst financial institutions to protect against the adverse effects of uncertainty caused by fluctuations in interest rates, exchange rates, commodity prices, and equity prices. New financial instruments and mathematical techniques are continuously developed and introduced in financial practice. These techniques are being used by an increasing number of firms, traders and financial risk managers across various industries. Risk and Financial Management: Mathematical and Computational Methods confronts the many issues and controversies, and explains the fundamental concepts that underpin financial risk management. Provides a comprehensive introduction to the core topics of risk and financial management. Adopts a pragmatic approach, focused on computational, rather than just theoretical, methods. Bridges the gap between theory and practice in financial risk management Includes coverage of utility theory, probability, options and derivatives, stochastic volatility and value at risk. Suitable for students of risk, mathematical finance, and financial risk management, and finance practitioners. Includes extensive reference lists, applications and suggestions for further reading. Risk and Financial Management: Mathematical and Computational Methods is ideally suited to both students of mathematical finance with little background in economics and finance, and students of financial risk management, as well as finance practitioners requiring a clearer understanding of the mathematical and computational methods they use every day. It combines the required level of rigor, to support the theoretical developments, with a practical flavour through many examples and applications.