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Sabr And Sabr Libor Market Models In Practice

Author: Christian Crispoldi
Publisher: Springer
ISBN: 1137378646
Size: 24.73 MB
Format: PDF, ePub, Mobi
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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: 9781119995630
Size: 66.43 MB
Format: PDF
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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

Financial Modelling

Author: Joerg Kienitz
Publisher: John Wiley & Sons
ISBN: 1118413296
Size: 34.80 MB
Format: PDF, ePub, Docs
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Financial Modelling - Theory, Implementation and Practice 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

Derivatives Analytics With Python Data Analytics Models Simulation Calibration And Hedging Ws

Author: Yves Hilpisch
Publisher: John Wiley & Sons
ISBN: 1119037999
Size: 73.54 MB
Format: PDF, Mobi
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Derivatives Analytics with Python: Data Analysis, Models, Simulation, Calibration and Hedging provides the necessary background information, theoretical foundations and numerical tools to implement a market-based valuation of stock index options. Topics are, amongst others, stylized facts of equity and options markets, risk-neutral valuation, Fourier transform methods, Monte Carlo simulation, model calibration, valuation and dynamic hedging. The financial models introduced in this book exhibit features like stochastic volatility, jump components and stochastic short rates. The approach is a practical one in that all important aspects are illustrated by a set of self-contained Python scripts. Benefits of Reading the Book: Data Analysis: Learn how to use Python for data and financial analysis. Reproduce major stylized facts of equity and options markets by yourself. Models: Learn risk-neutral pricing techniques from ground up, apply Fourier transform techniques to European options and advanced Monte Carlo pricing to American options. Simulation: Monte Carlo simulation is the most powerful and flexible numerical method for derivatives analytics. Simulate models with jumps, stochastic volatility and stochastic short rates. Calibration: Use global and local optimization techniques (incl. penalties) to calibrate advanced option pricing models to market quotes for options with different strikes and maturities. Hedging: Learn how to use advanced option pricing models in combination with advanced numerical methods to dynamically hedge American options. Python: All results, graphics, etc. presented are in general reproducible with the Python scripts accompanying the book. Benefit from more than 5,500 lines of code.

Novel Methods In Computational Finance

Author: Matthias Ehrhardt
Publisher: Springer
ISBN: 3319612824
Size: 62.67 MB
Format: PDF
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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.

The Validation Of Risk Models

Author: S. Scandizzo
Publisher: Springer
ISBN: 1137436964
Size: 50.65 MB
Format: PDF, ePub, Docs
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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.

Optimization Methods For Gas And Power Markets

Author: Enrico Edoli
Publisher: Springer
ISBN: 1137412976
Size: 26.76 MB
Format: PDF, ePub
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As power and gas markets are becoming more and more mature and globally competitive, the importance of reaching maximum potential economic efficiency is fundamental in all the sectors of the value chain, from investments selection to asset optimization, trading and sales. Optimization techniques can be used in many different fields of the energy industry, in order to reduce production and financial costs, increase sales revenues and mitigate all kinds of risks potentially affecting the economic margin. For this reason the industry has now focused its attention on the general concept of optimization and to the different techniques (mainly mathematical techniques) to reach it. Optimization Methods for Gas and Power Markets presents both theoretical elements and practical examples for solving energy optimization issues in gas and power markets. Starting with the theoretical framework and the basic business and economics of power and gas optimization, it quickly moves on to review the mathematical optimization problems inherent to the industry, and their solutions – all supported with examples from the energy sector. Coverage ranges from very long-term (and capital intensive) optimization problems such as investment valuation/diversification to asset (gas and power) optimization/hedging problems, and pure trading decisions. This book first presents the readers with various examples of optimization problems arising in power and gas markets, then deals with general optimization problems and describes the mathematical tools useful for their solution. The remainder of the book is dedicated to presenting a number of key business cases which apply the proposed techniques to concrete market problems. Topics include static asset optimization, real option evaluation, dynamic optimization of structured products like swing, virtual storage or virtual power plant contracts and optimal trading in intra-day power markets. As the book progresses, so too does the level of mathematical complexity, providing readers with an appreciation of the growing sophistication of even common problems in current market practice. Optimization Methods for Gas and Power Markets provides a valuable quantitative guide to the technicalities of optimization methodologies in gas and power markets; it is essential reading for practitioners in the energy industry and financial sector who work in trading, quantitative analysis and energy risk modeling.

The Libor Market Model In Practice

Author: Dariusz Gatarek
Publisher: John Wiley & Sons
ISBN: 9780470014431
Size: 64.53 MB
Format: PDF, Mobi
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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.

Advanced Quantitative Finance With C

Author: Alonso Peña, Ph.D.
Publisher: Packt Publishing Ltd
ISBN: 1782167234
Size: 47.45 MB
Format: PDF, ePub
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The book takes the reader through a fast but structured crash-course in quantitative finance, from theory to practice. If you are a quantitative analyst, risk manager, actuary, or a professional working in the field of quantitative finance and want a quick hands-on introduction to the pricing of financial derivatives, this book is ideal for you. You should be familiar with the basic programming concepts and C++ programming language. You should also be acquainted with calculus of undergraduate level.

Modern Derivatives Pricing And Credit Exposure Analysis

Author: Roland Lichters
Publisher: Springer
ISBN: 1137494840
Size: 20.77 MB
Format: PDF, Mobi
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This book provides a comprehensive guide for modern derivatives pricing and credit analysis. Written to provide sound theoretical detail but practical implication, it provides readers with everything they need to know to price modern financial derivatives and analyze the credit exposure of a financial instrument in today's markets.