Pde Valuation Of Interest Rate Derivatives
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Pde Valuation Of Interest Rate Derivatives
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Author : Peter Kohl-Landgraf
language : en
Publisher: BoD – Books on Demand
Release Date : 2007
Pde Valuation Of Interest Rate Derivatives written by Peter Kohl-Landgraf and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Derivative securities categories.
The Libor Market Model and its several extensions can be seen as state of the art in interest rate modeling. However, due to the ever increasing complexity of interest rate products, the high dimensionality of this approach starts to reach its limits from the computational side. This book is mainly concerned with a class of Markovian Yield Curve Models which try to overcome that disadvantage as they enable a low-dimensional deterministic and fast PDE valuation. The objective of this book is thereby threefold: - To illuminate in a compact way the connection between stochastic processes and partial differential equations as well as review the key features of arbitrage-free pricing. - To embed the here analyzed Markovian model class into the entire framework of interest rate models. - To present and implement robust numerical schemes, which enable an efficient computational treatment of risk-neutral product valuation by using PDE methods.
Interest Rate Derivatives
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Author : Ingo Beyna
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-20
Interest Rate Derivatives written by Ingo Beyna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Mathematics categories.
The class of interest rate models introduced by O. Cheyette in 1994 is a subclass of the general HJM framework with a time dependent volatility parameterization. This book addresses the above mentioned class of interest rate models and concentrates on the calibration, valuation and sensitivity analysis in multifactor models. It derives analytical pricing formulas for bonds and caplets and applies several numerical valuation techniques in the class of Cheyette model, i.e. Monte Carlo simulation, characteristic functions and PDE valuation based on sparse grids. Finally it focuses on the sensitivity analysis of Cheyette models and derives Model- and Market Greeks. To the best of our knowledge, this sensitivity analysis of interest rate derivatives in the class of Cheyette models is unique in the literature. Up to now the valuation of interest rate derivatives using PDEs has been restricted to 3 dimensions only, since the computational effort was too great. The author picks up the sparse grid technique, adjusts it slightly and can solve high-dimensional PDEs (four dimensions plus time) accurately in reasonable time. Many topics investigated in this book are new areas of research and make a significant contribution to the scientific community of financial engineers. They also represent a valuable development for practitioners.
Derivative Securities And Difference Methods
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Author : You-lan Zhu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-04
Derivative Securities And Difference Methods written by You-lan Zhu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-04 with Mathematics categories.
This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts. In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with details. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems. In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products. This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods in financial derivatives. For this new edition, the book has been updated throughout with many new problems added. More details about numerical methods for some options, for example, Asian options with discrete sampling, are provided and the proof of solution-uniqueness of derivative security problems and the complete stability analysis of numerical methods for two-dimensional problems are added. Review of first edition: “...the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS
Efficient Methods For Valuing Interest Rate Derivatives
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Author : Antoon Pelsser
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Efficient Methods For Valuing Interest Rate Derivatives written by Antoon Pelsser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore a host of practical issues.
Interest Rate Dynamics Derivatives Pricing And Risk Management
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Author : Lin Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Interest Rate Dynamics Derivatives Pricing And Risk Management written by Lin Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
There are two types of tenn structure models in the literature: the equilibrium models and the no-arbitrage models. And there are, correspondingly, two types of interest rate derivatives pricing fonnulas based on each type of model of the tenn structure. The no-arbitrage models are characterized by the work of Ho and Lee (1986), Heath, Jarrow, and Morton (1992), Hull and White (1990 and 1993), and Black, Dennan and Toy (1990). Ho and Lee (1986) invent the no-arbitrage approach to the tenn structure modeling in the sense that the model tenn structure can fit the initial (observed) tenn structure of interest rates. There are a number of disadvantages with their model. First, the model describes the whole volatility structure by a sin gle parameter, implying a number of unrealistic features. Furthennore, the model does not incorporate mean reversion. Black-Dennan-Toy (1990) develop a model along tbe lines of Ho and Lee. They eliminate some of the problems of Ho and Lee (1986) but create a new one: for a certain specification of the volatility function, the short rate can be mean-fteeting rather than mean-reverting. Heath, Jarrow and Morton (1992) (HJM) construct a family of continuous models of the term struc ture consistent with the initial tenn structure data.
Pricing And Trading Interest Rate Derivatives
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Author : J Hamish M Darbyshire
language : en
Publisher: Aitch & Dee Limited
Release Date : 2022-08-07
Pricing And Trading Interest Rate Derivatives written by J Hamish M Darbyshire and has been published by Aitch & Dee Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-07 with categories.
The most professional and industry relatable text currently available for linear interest rate derivatives. Written by a practicing derivatives portfolio manager with over fifteen years of fixed income trading experience, this book focuses on core trading concepts; pricing, curve building (single and multi-currency), risk, credit and CSAs, regulations, VaR and PCA, volatility, cross-gamma, trade strategy analysis and market moving influences. The book's focus is interest rate swaps and cross-currency swaps, updated for a risk free rate (RFR, such as SOFR and ESTR) framework as opposed to LIBOR. Topics are presented from that perspective, outlining the importance of regulations in an IRD capacity, with volatility and swaptions taught from a practical point of view rather than an overly cumbersome academic one. This third edition (2022) markedly expands the second edition (2017), by not only providing extensive analysis but also building up a modern codebase, step-by-step, in Python. It constructs and solves interest rate curves and goes on to implement risk and cross-gamma calculations, demonstrating the implementation of automatic differentiation for superior efficiency. Read more at https: //github.com/attack68/book_irds3. The treatment of risk is expansive and thorough. The author formally analyses modern market-maker techniques to accurately predict PnL, and successfully implement multiple, consistent perspectives to view all details of risks. Almost everything included here is compulsory knowledge for a modern, successful, swaps trader or interest rate risk portfolio manager. Certainly this book sets the benchmark for the level of expertise that swaps traders should strive for, and the style is aimed at the novice and professional alike.
Interest Rate Swaps And Their Derivatives
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Author : Amir Sadr
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-09
Interest Rate Swaps And Their Derivatives written by Amir Sadr and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-09 with Business & Economics categories.
An up-to-date look at the evolution of interest rate swaps and derivatives Interest Rate Swaps and Derivatives bridges the gap between the theory of these instruments and their actual use in day-to-day life. This comprehensive guide covers the main "rates" products, including swaps, options (cap/floors, swaptions), CMS products, and Bermudan callables. It also covers the main valuation techniques for the exotics/structured-notes area, which remains one of the most challenging parts of the market. Provides a balance of relevant theory and real-world trading instruments for rate swaps and swap derivatives Uses simple settings and illustrations to reveal key results Written by an experienced trader who has worked with swaps, options, and exotics With this book, author Amir Sadr shares his valuable insights with practitioners in the field of interest rate derivatives-from traders and marketers to those in operations.
Dynamic Term Structure Modeling
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Author : Sanjay K. Nawalkha
language : en
Publisher: John Wiley & Sons
Release Date : 2007-05-23
Dynamic Term Structure Modeling written by Sanjay K. Nawalkha and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-23 with Business & Economics categories.
Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling
A Highly Efficient Implementation On Gpu Clusters Of Pde Based Pricing Methods For Path Dependent Foreign Exchange Interest Rate Derivatives
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Author : Duy-Minh Dang
language : en
Publisher:
Release Date : 2013
A Highly Efficient Implementation On Gpu Clusters Of Pde Based Pricing Methods For Path Dependent Foreign Exchange Interest Rate Derivatives written by Duy-Minh Dang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
We present a highly efficient parallelization of the computation of the price of exotic cross-currency interest rate derivatives with path-dependent features via a Partial Differential Equation (PDE) approach. In particular, we focus on the parallel pricing on Graphics Processing Unit (GPU) clusters of long-dated foreign exchange (FX) interest rate derivatives, namely Power-Reverse Dual-Currency (PRDC) swaps with FX Target Redemption (FX-TARN) features under a three-factor model. Challenges in pricing these derivatives via a PDE approach arise from the high-dimensionality of the model PDE, as well as from path-dependency of the FX-TARN feature. The PDE pricing framework for FX-TARN PRDC swaps is based on partitioning the pricing problem into several independent pricing sub-problems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Finite difference methods on non-uniform grids are used for the spatial discretization of the PDE, and the Alternating Direction Implicit (ADI) technique is employed for the time discretization. Our implementation of the pricing procedure on a GPU cluster involves (i) efficiently solving each independent sub-problems on a GPU via a parallelization of the ADI timestepping technique, and (ii) utilizing MPI for the communication between pricing processes at the end of the time period of the swap's tenor structure. Numerical results showing the efficiency of the parallel methods are provided.
Fixed Income And Interest Rate Derivative Analysis
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Author : Mark Britten-Jones
language : en
Publisher: Elsevier
Release Date : 1998-10-15
Fixed Income And Interest Rate Derivative Analysis written by Mark Britten-Jones and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-15 with Business & Economics categories.
Fixed Income and Interest Rate Derivative Analysis gives a clear and accessible approach to the analytical techniques of debt instrument valuation. Without using complicated mathematical abstractions, this text shows that the fundamentals of fixed income and interest rate derivate analysis can be easily understood when seen as a small number of simple economic concepts. Concepts inroduced in this book are reinforced and explained, not with the use of high-powered mathematics, but with actual examples of various market instruments and case studies from North America, Europe, Australia and Hong Kong. The text also contains review questions which aid the reader in their understanding. Mark Britten-Jones, BEcon, MA, PhD, is an Assistant Professor of Finance at the London Business School where he teaches Fixed Income Securities and Markets as part of a MBA and Master's course in Finance. A comprehensive and accessible explanation of underlying theory, and its practical application Case studies and worked examples from around the world's capital markets How to use spreadsheet modelling in fixed income and interest rate derivative valuation