Sabr And Sabr Libor Market Models In Practice

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SABR and SABR LIBOR Market Models in Practice

Author : Christian Crispoldi
Publisher : Springer
ISBN 13 : 1137378646
Total Pages : 274 pages
Book Rating : 4.1/5 (373 download)

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Book Synopsis SABR and SABR LIBOR Market Models in Practice by : Christian Crispoldi

Download or read book SABR and SABR LIBOR Market Models in Practice written by Christian Crispoldi and published by Springer. This book was released on 2016-04-29 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate traders have been using the SABR model to price vanilla products for more than a decade. However this model suffers however from a severe limitation: its inability to value exotic products. A term structure model à la LIBOR Market Model (LMM) is often employed to value these more complex derivatives, however the LMM is unable to capture the volatility smile. A joint SABR LIBOR Market Model is the natural evolution towards a consistent pricing of vanilla and exotic products. Knowledge of these models is essential to all aspiring interest rate quants, traders and risk managers, as well an understanding of their failings and alternatives. SABR and SABR Libor Market Models in Practice is an accessible guide to modern interest rate modelling. Rather than covering an array of models which are seldom used in practice, it focuses on the SABR model, the market standard for vanilla products, the LIBOR Market Model, the most commonly used model for exotic products and the extended SABR LIBOR Market Model. The book takes a hands-on approach, demonstrating simply how to implement and work with these models in a market setting. It bridges the gap between the understanding of the models from a conceptual and mathematical perspective and the actual implementation by supplementing the interest rate theory with modelling specific, practical code examples written in Python.

SABR and SABR LIBOR Market Models in Practice

Author : Christian Crispoldi
Publisher : Palgrave Macmillan
ISBN 13 : 9781349571772
Total Pages : 216 pages
Book Rating : 4.5/5 (717 download)

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Book Synopsis SABR and SABR LIBOR Market Models in Practice by : Christian Crispoldi

Download or read book SABR and SABR LIBOR Market Models in Practice written by Christian Crispoldi and published by Palgrave Macmillan. This book was released on 2014-01-14 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate traders have been using the SABR model to price vanilla products for more than a decade. However this model suffers however from a severe limitation: its inability to value exotic products. A term structure model à la LIBOR Market Model (LMM) is often employed to value these more complex derivatives, however the LMM is unable to capture the volatility smile. A joint SABR LIBOR Market Model is the natural evolution towards a consistent pricing of vanilla and exotic products. Knowledge of these models is essential to all aspiring interest rate quants, traders and risk managers, as well an understanding of their failings and alternatives. SABR and SABR Libor Market Models in Practice is an accessible guide to modern interest rate modelling. Rather than covering an array of models which are seldom used in practice, it focuses on the SABR model, the market standard for vanilla products, the LIBOR Market Model, the most commonly used model for exotic products and the extended SABR LIBOR Market Model. The book takes a hands-on approach, demonstrating simply how to implement and work with these models in a market setting. It bridges the gap between the understanding of the models from a conceptual and mathematical perspective and the actual implementation by supplementing the interest rate theory with modelling specific, practical code examples written in Python.

The SABR/LIBOR Market Model

Author : Riccardo Rebonato
Publisher : John Wiley & Sons
ISBN 13 : 1119995639
Total Pages : 308 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis The SABR/LIBOR Market Model by : Riccardo Rebonato

Download or read book The SABR/LIBOR Market Model written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options. The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced. Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress

SABR and SABR LIBOR Market Models in Practice

Author : Christian Crispoldi
Publisher : Springer
ISBN 13 : 1137378646
Total Pages : 238 pages
Book Rating : 4.1/5 (373 download)

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Book Synopsis SABR and SABR LIBOR Market Models in Practice by : Christian Crispoldi

Download or read book SABR and SABR LIBOR Market Models in Practice written by Christian Crispoldi and published by Springer. This book was released on 2016-04-29 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate traders have been using the SABR model to price vanilla products for more than a decade. However this model suffers however from a severe limitation: its inability to value exotic products. A term structure model à la LIBOR Market Model (LMM) is often employed to value these more complex derivatives, however the LMM is unable to capture the volatility smile. A joint SABR LIBOR Market Model is the natural evolution towards a consistent pricing of vanilla and exotic products. Knowledge of these models is essential to all aspiring interest rate quants, traders and risk managers, as well an understanding of their failings and alternatives. SABR and SABR Libor Market Models in Practice is an accessible guide to modern interest rate modelling. Rather than covering an array of models which are seldom used in practice, it focuses on the SABR model, the market standard for vanilla products, the LIBOR Market Model, the most commonly used model for exotic products and the extended SABR LIBOR Market Model. The book takes a hands-on approach, demonstrating simply how to implement and work with these models in a market setting. It bridges the gap between the understanding of the models from a conceptual and mathematical perspective and the actual implementation by supplementing the interest rate theory with modelling specific, practical code examples written in Python.

Market Practice In Financial Modelling

Author : Chia Chiang Tan
Publisher : World Scientific Publishing Company
ISBN 13 : 9814434582
Total Pages : 439 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Market Practice In Financial Modelling by : Chia Chiang Tan

Download or read book Market Practice In Financial Modelling written by Chia Chiang Tan and published by World Scientific Publishing Company. This book was released on 2012-07-11 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to bridge the gap between foundational quantitative finance and market practice, this book goes beyond the basics covered in most textbooks by presenting content concerning actual industry norms, thus resulting in a clearer picture of the field for the readers. These include, for instance, the practitioner's perspective of how local versus stochastic volatility affects forward smile, or the implications of mean reversion on forward volatility.Key considerations for modelling in rates, equities and foreign exchange are presented from the perspective of common themes across various assets, as well as their individual characteristics.The discussion on models emphasizes the key aspects that are relevant to the pricing of different types of financial derivatives, so that the reader can observe how an appropriate choice of models is essential in reflecting the risk profile and hedging considerations for different products.With the knowledge gleaned from this book, readers will attain a more comprehensive understanding of market practice in derivatives modelling.

Interest Rate Derivatives Explained: Volume 2

Author : Jörg Kienitz
Publisher : Springer
ISBN 13 : 1137360194
Total Pages : 261 pages
Book Rating : 4.1/5 (373 download)

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Book Synopsis Interest Rate Derivatives Explained: Volume 2 by : Jörg Kienitz

Download or read book Interest Rate Derivatives Explained: Volume 2 written by Jörg Kienitz and published by Springer. This book was released on 2017-11-08 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on Interest Rate Derivatives has three parts. The first part is on financial products and extends the range of products considered in Interest Rate Derivatives Explained I. In particular we consider callable products such as Bermudan swaptions or exotic derivatives. The second part is on volatility modelling. The Heston and the SABR model are reviewed and analyzed in detail. Both models are widely applied in practice. Such models are necessary to account for the volatility skew/smile and form the fundament for pricing and risk management of complex interest rate structures such as Constant Maturity Swap options. Term structure models are introduced in the third part. We consider three main classes namely short rate models, instantaneous forward rate models and market models. For each class we review one representative which is heavily used in practice. We have chosen the Hull-White, the Cheyette and the Libor Market model. For all the models we consider the extensions by a stochastic basis and stochastic volatility component. Finally, we round up the exposition by giving an overview of the numerical methods that are relevant for successfully implementing the models considered in the book.

Financial Modelling

Author : Joerg Kienitz
Publisher : John Wiley & Sons
ISBN 13 : 0470744898
Total Pages : 736 pages
Book Rating : 4.4/5 (77 download)

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Book Synopsis Financial Modelling by : Joerg Kienitz

Download or read book Financial Modelling written by Joerg Kienitz and published by John Wiley & Sons. This book was released on 2013-02-18 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial modelling Theory, Implementation and Practice with MATLAB Source Jörg Kienitz and Daniel Wetterau Financial Modelling - Theory, Implementation and Practice with MATLAB Source is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk-neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes. Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk. The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor market model. Source code used for producing the results and analysing the models is provided on the author's dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981.

Calibration of Libor Market Model to Caps and Swaptions Market Volatilities

Author : Natalia Bandera
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Calibration of Libor Market Model to Caps and Swaptions Market Volatilities by : Natalia Bandera

Download or read book Calibration of Libor Market Model to Caps and Swaptions Market Volatilities written by Natalia Bandera and published by . This book was released on 2008 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We show a particular case of joint calibration of the Libor Market Model (LMM) to market-quoted implied cap and swaption volatilities using a linear-exponential parameterization. We also create a Monte Carlo vanilla swaption-pricing engine using the model in the first part of the paper. In the second part of the paper, an attempt will be made to incorporate the dynamics of the volatility skew for caplets though implementation of stochastic volatility SABR model.

The LIBOR Market Model in Practice

Author : Dariusz Gatarek
Publisher : John Wiley & Sons
ISBN 13 : 0470060417
Total Pages : 290 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis The LIBOR Market Model in Practice by : Dariusz Gatarek

Download or read book The LIBOR Market Model in Practice written by Dariusz Gatarek and published by John Wiley & Sons. This book was released on 2007-01-30 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives. This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.

Novel Methods in Computational Finance

Author : Matthias Ehrhardt
Publisher : Springer
ISBN 13 : 3319612824
Total Pages : 599 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Novel Methods in Computational Finance by : Matthias Ehrhardt

Download or read book Novel Methods in Computational Finance written by Matthias Ehrhardt and published by Springer. This book was released on 2017-09-19 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector. The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models. In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry. Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.

Interest Rate Modeling

Author : Lixin Wu
Publisher : CRC Press
ISBN 13 : 1351227416
Total Pages : 494 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Interest Rate Modeling by : Lixin Wu

Download or read book Interest Rate Modeling written by Lixin Wu and published by CRC Press. This book was released on 2019-03-04 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing many results that are new, or which exist only in recent research articles, Interest Rate Modeling: Theory and Practice, 2nd Edition 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 approach, and handles option evaluations with precise numerical methods. Features Presents a complete cycle of model construction and applications, showing readers how to build and use models Provides a systematic treatment of intriguing industrial issues, such as volatility and correlation adjustments Contains exercise sets and a number of examples, with many based on real market data Includes comments on cutting-edge research, such as volatility-smile, positive interest-rate models, and convexity adjustment New to the 2nd edition: volatility smile modeling; a new paradigm for inflation derivatives modeling; an extended market model for credit derivatives; a dual-curved model for the post-crisis interest-rate derivatives markets; and an elegant framework for the xVA.

Interest Rate Models - Theory and Practice

Author : Damiano Brigo
Publisher : Springer Science & Business Media
ISBN 13 : 354034604X
Total Pages : 1016 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Interest Rate Models - Theory and Practice by : Damiano Brigo

Download or read book Interest Rate Models - Theory and Practice written by Damiano Brigo and published by Springer Science & Business Media. This book was released on 2007-09-26 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modern SABR Analytics

Author : Alexandre Antonov
Publisher : Springer
ISBN 13 : 303010656X
Total Pages : 127 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Modern SABR Analytics by : Alexandre Antonov

Download or read book Modern SABR Analytics written by Alexandre Antonov and published by Springer. This book was released on 2019-04-23 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent manner. It extends SABR to a negative rates environment, and shows how to generalize it to a similar model with additional degrees of freedom, allowing simultaneous model calibration to swaptions and CMSs. Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia. Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.

No-Arbitrage Dynamics for a Tractable SABR Term Structure Libor Model

Author : Massimo Morini
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis No-Arbitrage Dynamics for a Tractable SABR Term Structure Libor Model by : Massimo Morini

Download or read book No-Arbitrage Dynamics for a Tractable SABR Term Structure Libor Model written by Massimo Morini and published by . This book was released on 2016 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The SABR closed-form formula (Hagan et. al 2002) is the standard for smile-consistent pricing in the swaption market. Here we address the issue of turning SABR assumptions into a consistent and arbitrage-free term structure model in the BGM/Libor Market Model framework. We compute the joint dynamics followed by Libor rates and stochastic volatility of SABR kind under the general pricing measures used for interest rate derivatives, and we observe that the volatility dynamics is non-standard. Based on the analysis of the equation found, we develop and justify theoretically a few approximations aimed at making these no-arbitrage dynamics compatible with the use of the SABR closed-form formula. Then the formulas developed above are confronted both with alternative numerical implementations and with market data. We verify that the formulas for no-arbitrage corrections are acceptably precise, maintain good fitting, and produce regular Libor parameters. Finally we verify that the no-arbitrage corrections to the volatility dynamics make the out-of-calibration-sample prices implied by the model closer to market quotations, compared to prices implied by a trivial multivariate SABR neglecting such corrections.

The LIBOR Market Model in Practice

Author : Dariusz Gatarek
Publisher : John Wiley & Sons
ISBN 13 : 9780470014431
Total Pages : 0 pages
Book Rating : 4.0/5 (144 download)

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Book Synopsis The LIBOR Market Model in Practice by : Dariusz Gatarek

Download or read book The LIBOR Market Model in Practice written by Dariusz Gatarek and published by John Wiley & Sons. This book was released on 2007-01-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives. This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.

Discounting, LIBOR, CVA and Funding

Author : C. Kenyon
Publisher : Springer
ISBN 13 : 1137268522
Total Pages : 280 pages
Book Rating : 4.1/5 (372 download)

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Book Synopsis Discounting, LIBOR, CVA and Funding by : C. Kenyon

Download or read book Discounting, LIBOR, CVA and Funding written by C. Kenyon and published by Springer. This book was released on 2012-08-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing the most up-to-date tools and techniques for pricing interest rate and credit products for the new financial world, this book discusses pricing and hedging, funding and regulation, and interpretation, as an essential resource for quantitatively minded practitioners and researchers in finance.

The Validation of Risk Models

Author : S. Scandizzo
Publisher : Springer
ISBN 13 : 1137436964
Total Pages : 242 pages
Book Rating : 4.1/5 (374 download)

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Book Synopsis The Validation of Risk Models by : S. Scandizzo

Download or read book The Validation of Risk Models written by S. Scandizzo and published by Springer. This book was released on 2016-07-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a one-stop-shop reference for risk management practitioners involved in the validation of risk models. It is a comprehensive manual about the tools, techniques and processes to be followed, focused on all the models that are relevant in the capital requirements and supervisory review of large international banks.