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Series Expansion Of The Sabr Joint Density
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Book Synopsis Series Expansion of the SABR Joint Density by : Qi Wu
Download or read book Series Expansion of the SABR Joint Density written by Qi Wu and published by . This book was released on 2015 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under the SABR stochastic volatility model, pricing and hedging contracts that are sensitive to forward smile risk (e.g., forward starting options, barrier options) require the joint transition density.In this paper, we address this problem by providing closed-form representations, asymptotically, of the joint transition density. Specifically, we construct an expansion of the joint density through a hierarchy of parabolic equations after applying total volatility-of-volatility scaling and a near-Gaussian coordinate transformation. We then established an existence result to characterize the truncation error and provide explicit joint density formulas for the first three orders. Our approach inherits the same spirit of a small total volatility-of-volatility assumption as in in the original SABR analysis. Our results for the joint transition density serve as a basis for managing forward smile risk. Through numerical experiments, we illustrate the accuracy of our expansion in terms of joint density, marginal density, probability mass and implied volatilities for European call options.
Book Synopsis Finance at Fields by : Matheus R. Grasselli
Download or read book Finance at Fields written by Matheus R. Grasselli and published by World Scientific. This book was released on 2013 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding collection of articles includes papers presented at the Fields Institute, Toronto, as part of the Thematic Program in Quantitative Finance that took place in the first six months of the year 2010. The scope of the volume in very broad, including papers on foundational issues in mathematical finance, papers on computational finance, and papers on derivatives and risk management. Many of the articles contain path-breaking insights that are relevant to the developing new order of post-crisis financial risk management.
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.
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.
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 2019-05-02 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.
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.
Book Synopsis Option Valuation Under Stochastic Volatility II by : Alan L. Lewis
Download or read book Option Valuation Under Stochastic Volatility II written by Alan L. Lewis and published by . This book was released on 2016-05-12 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to the author's well-received "Option Valuation under Stochastic Volatility." It extends that work to jump-diffusions and many related topics in quantitative finance. Topics include spectral theory for jump-diffusions, boundary behavior for short-term interest rate models, modelling VIX options, inference theory, discrete dividends, and more. It provides approximately 750 pages of original research in 26 chapters, with 165 illustrations, Mathematica, and some C/C++ codes. The first 12 chapters (550 pages) are completely new. Also included are reprints of selected previous publications of the author for convenient reference. The book should interest both researchers and quantitatively-oriented investors and traders. First 12 chapters: Slow Reflection, Jump-Returns, & Short-term Interest Rates Spectral Theory for Jump-diffusions Joint Time Series Modelling of SPX and VIX Modelling VIX Options (and Futures) under Stochastic Volatility Stochastic Volatility as a Hidden Markov Model Continuous-time Inference: Mathematical Methods and Worked Examples A Closer Look at the Square-root and 3/2-model A Closer Look at the SABR Model Back to Basics: An Update on the Discrete Dividend Problem PDE Numerics without the Pain Exact Solution to Double Barrier Problems under a Class of Processes Advanced Smile Asymptotics: Geometry, Geodesics, and All That
Book Synopsis Stereotactic Body Radiation Therapy by : Simon S. Lo
Download or read book Stereotactic Body Radiation Therapy written by Simon S. Lo and published by Springer Science & Business Media. This book was released on 2012-08-28 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stereotactic body radiation therapy (SBRT) has emerged as an important innovative treatment for various primary and metastatic cancers. This book provides a comprehensive and up-to-date account of the physical/technological, biological, and clinical aspects of SBRT. It will serve as a detailed resource for this rapidly developing treatment modality. The organ sites covered include lung, liver, spine, pancreas, prostate, adrenal, head and neck, and female reproductive tract. Retrospective studies and prospective clinical trials on SBRT for various organ sites from around the world are examined, and toxicities and normal tissue constraints are discussed. This book features unique insights from world-renowned experts in SBRT from North America, Asia, and Europe. It will be necessary reading for radiation oncologists, radiation oncology residents and fellows, medical physicists, medical physics residents, medical oncologists, surgical oncologists, and cancer scientists.
Book Synopsis Large Deviations and Asymptotic Methods in Finance by : Peter K. Friz
Download or read book Large Deviations and Asymptotic Methods in Finance written by Peter K. Friz and published by Springer. This book was released on 2015-06-16 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.
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
Book Synopsis Stochastic Volatility Modeling by : Lorenzo Bergomi
Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by CRC Press. This book was released on 2015-12-16 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Book Synopsis Introduction to Malliavin Calculus by : David Nualart
Download or read book Introduction to Malliavin Calculus written by David Nualart and published by Cambridge University Press. This book was released on 2018-09-27 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
Book Synopsis Analysis, Geometry, and Modeling in Finance by : Pierre Henry-Labordere
Download or read book Analysis, Geometry, and Modeling in Finance written by Pierre Henry-Labordere and published by CRC Press. This book was released on 2008-09-22 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th
Book Synopsis The Federal Reserve System Purposes and Functions by : Board of Governors of the Federal Reserve System
Download or read book The Federal Reserve System Purposes and Functions written by Board of Governors of the Federal Reserve System and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an in-depth overview of the Federal Reserve System, including information about monetary policy and the economy, the Federal Reserve in the international sphere, supervision and regulation, consumer and community affairs and services offered by Reserve Banks. Contains several appendixes, including a brief explanation of Federal Reserve regulations, a glossary of terms, and a list of additional publications.
Book Synopsis Handbook of Financial Risk Management by : Thierry Roncalli
Download or read book Handbook of Financial Risk Management written by Thierry Roncalli and published by CRC Press. This book was released on 2020-04-23 with total page 987 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed over 20 years of teaching academic courses, the Handbook of Financial Risk Management can be divided into two main parts: risk management in the financial sector; and a discussion of the mathematical and statistical tools used in risk management. This comprehensive text offers readers the chance to develop a sound understanding of financial products and the mathematical models that drive them, exploring in detail where the risks are and how to manage them. Key Features: Written by an author with both theoretical and applied experience Ideal resource for students pursuing a master’s degree in finance who want to learn risk management Comprehensive coverage of the key topics in financial risk management Contains 114 exercises, with solutions provided online at www.crcpress.com/9781138501874
Book Synopsis Modern Computational Finance by : Antoine Savine
Download or read book Modern Computational Finance written by Antoine Savine and published by John Wiley & Sons. This book was released on 2018-11-20 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arguably the strongest addition to numerical finance of the past decade, Algorithmic Adjoint Differentiation (AAD) is the technology implemented in modern financial software to produce thousands of accurate risk sensitivities, within seconds, on light hardware. AAD recently became a centerpiece of modern financial systems and a key skill for all quantitative analysts, developers, risk professionals or anyone involved with derivatives. It is increasingly taught in Masters and PhD programs in finance. Danske Bank's wide scale implementation of AAD in its production and regulatory systems won the In-House System of the Year 2015 Risk award. The Modern Computational Finance books, written by three of the very people who designed Danske Bank's systems, offer a unique insight into the modern implementation of financial models. The volumes combine financial modelling, mathematics and programming to resolve real life financial problems and produce effective derivatives software. This volume is a complete, self-contained learning reference for AAD, and its application in finance. AAD is explained in deep detail throughout chapters that gently lead readers from the theoretical foundations to the most delicate areas of an efficient implementation, such as memory management, parallel implementation and acceleration with expression templates. The book comes with professional source code in C++, including an efficient, up to date implementation of AAD and a generic parallel simulation library. Modern C++, high performance parallel programming and interfacing C++ with Excel are also covered. The book builds the code step-by-step, while the code illustrates the concepts and notions developed in the book.
Book Synopsis Option Valuation Under Stochastic Volatility by : Alan L. Lewis
Download or read book Option Valuation Under Stochastic Volatility written by Alan L. Lewis and published by . This book was released on 2000 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
